MediaWiki API result
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{
"compare": {
"fromid": 1,
"fromrevid": 1,
"fromns": 0,
"fromtitle": "Itulau Muamua",
"toid": 2,
"torevid": 2,
"tons": 0,
"totitle": "Fa'ailoga masani",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">Line 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">Line 1:</td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><<del class=\"diffchange diffchange-inline\">strong</del>><del class=\"diffchange diffchange-inline\">MediaWiki has been installed</del>.</<del class=\"diffchange diffchange-inline\">strong</del>></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><<ins class=\"diffchange diffchange-inline\">math display=\"block\"</ins>><ins class=\"diffchange diffchange-inline\">2,\\ 4,\\ 4,\\ 4,\\ 5,\\ 5,\\ 7,\\ 9</ins>.</<ins class=\"diffchange diffchange-inline\">math</ins>></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Standard_deviation_diagram.svg|thumb| O se molipi o le taugofiega o ni suiga (pe o le kuriva o le iga) i lea i le vaega uma ua fa'atino ai le tele o ni suiga o le ulufalega 1 tauina - Vaai foi: 68\u201395\u201399.7 fa'atino.]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Normal-distribution-cumulative-density-function.svg|thumb| Fa'atupu fa'aopoopoina o se tufatufaga masani ma le tau fa'amoemoeina 0 ma le va'aiga masani 1]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le su\u2019esu\u2019e, le fa\u2019amaoniga matu\u0101 o se mea fa\u02bbata\u02bbita\u02bbiga e fa\u2019aaogaina mo le fuafuaga pe aisea e tu\u02bbuina ai pe aisea e fa\u02bbaaogaina ai le isi tulaga o mea.[1] O le su\u2019esu\u2019e tele e fa\u2019apea o le vaega o le la\u02bbititi po\u02bbo le tafa e fa\u2019atautaia ai nisi o fesili.[1] O le su\u2019esu\u2019e tele lea na fa\u02bbaaogaina ina ia fa\u02bbapea lea o le mafuaaga na tatau ona ia teuteu i le itu o le meana (peita\u2019i o le mana\u02bbomia o le a\u02bbafiaga) o le mea, ae maise o le su\u2019esu\u2019e tele, o le mafuaaga na fa\u02bbapea lea o le tafa e fa\u02bbatautaia ai nisi o fesili e pei ona uma i luga o se lona la\u02bbititi.</ins></div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User</del>'<del class=\"diffchange diffchange-inline\">s Guide] for information on using the wiki software</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E mafai ona su\u2019esu\u2019eina le su\u2019esu\u2019e tele i le SD, ma o se fa\u02bbailoga masani i tusi aloaia ma mea mataupu e fa\u02bbaaogaina ai le itulau o le sigana Greeki ma le </ins>'<ins class=\"diffchange diffchange-inline\">\u03c3' (sigma), mo le su\u2019esu\u2019e tele o le atunuu, po\u02bbo le itulau o le li\u2019a, mo le su\u2019esu\u2019e tele o le amo</ins>.</div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>== <del class=\"diffchange diffchange-inline\">Getting started </del>==</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Le su\u2019esu\u2019e tele o se mea o loo faitauina ai le varaieti o se mea, sae le tu\u02bbuina le su\u2019esu\u2019e matu\u0101 o le mea o le tele. O lea o se ata o le alamuiti lea l\u0113 malilie, ae i le aufaigaluega lagona, e l\u0113 fa\u02bbamoemoe. [2][3] O se a\u02bboa\u02bbo na iai le su\u2019esu\u2019e tele o se mea e le mafai ona amatalia lea e le vala\u02bbau ma le data.</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual</del>:<del class=\"diffchange diffchange-inline\">Configuration_settings Configuration settings list</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special:MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual</del>:<del class=\"diffchange diffchange-inline\">FAQ MediaWiki FAQ</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le fa'agaioiga fa'atupu o se populasi po'o se s\u0101mple ma le fa'agaioiga o se setatistic (e.g., o le s\u0101mple mean) o lo'o m\u0101tu\u0101 ma le fa'ailoa o lelei. O le fa'agaioiga lelei o le mean o le s\u0101mple o le standard error o le population, e le'i tatau ona vaega i le standard deviation o le set\u0101 o mea na fa'asaoina ma le fai se mean mo ia s\u0101mple. O le standard error o le mean e fa'apea atu i le population standard deviation fa'atasi ai ma le square root o le malo s\u0101mple, ma e a'oa'oina i le a'oa'oina o le s\u0101mple standard deviation fa'atasi ai ma le square root o le malo s\u0101mple. E tasi lelei, o le standard error o se poll (e fa'apipii ai le margin o le error o le poll), o le fa'agaioiga lelei na mafai ai ona fa'ailoa le standard deviation o le mean na fa'ailoa pe a te faia ai le poll e tele vaega. Ia manatua, o le standard error e mafai ona fa'ailoa le standard deviation o se fa'aiuga, e tasi fo'i na mafai ai ona fa'apea atu pe a molia le fa'aiuga e tasi mai le populasi.</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">postorius</del>/<del class=\"diffchange diffchange-inline\">lists</del>/<del class=\"diffchange diffchange-inline\">mediawiki</del>-<del class=\"diffchange diffchange-inline\">announce</del>.<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org/ MediaWiki release mailing list</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* </del>[<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Localisation#Translation_resources Localise MediaWiki for your language]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le tamaoaiga, o le matamata fa'atino e fa'ailoa ai le fa'agaioiga o le data (e tasi leaga ma le s\u0101mple taimi) ma le fa'agaioiga o le estimate (e tasi leaga ma le mafua'aga o le fa'aiuga). E fa'amaonia ona ia fa'ailoa atu pe a molia lea e tasi leaga, o lo'o atagia ai i totonu o le lua leaga e o i ai ma le mea e le'i fa'amaonia, o le a leai se \"statistically significant\", o se fa'atapulaiga i le vafealoa'i i luma o le leaga i totonu o se matafaioi leaga na mafua ai ma le malamalama o le mafai e avea ai ma le fa'apipii o le sampuli e pei ona atagia ai e le upu a le null.</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* [https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual</del>:<del class=\"diffchange diffchange-inline\">Combating_spam Learn how to combat spam on your wiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ina ua iai le s\u0101mple o data mai le populasi, o le upu \"standard deviation\" o le s\u0101mple po'o le sample standard deviation e mafai ona fa'apea atu i le taua luga, e tusa ma le fa'agaioiga a luga i ai ma le latou data, po'o se taua fa'apipi'i na mafai ona fa'ailoa e a'oa'oina ai le standard deviation o le populasi (le fa'agaioiga o le populasi atoa).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Fa'ata'ita'iga fa'avae ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fuainumera masani o le faitau aofa'i o togi o tamaiti e to'avalu ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Aumoega atu o le fa'agaioiga o le populasi atoa, o leitioata o le fa'agaioiga o le populasi e mafai ona mauaina ma le faitauina o le square root o le avea o le tali o lea mea na faitauina e avea ai ma le avea o le tali o mea ua tu'uina mai i le uta'i o lea mea na faitauina. O a lea, o tagata vala'au a le tulaga o le fa'agaioiga o le populasi atoa o vala'au i lalo:<math display=\"block\"> \\mu = \\frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = \\frac{40}{8} = 5. </math>O nei valu e wara i le lenei, e i ai le mea (average) o le 5:<math display=\"block\">\\begin{array}{lll}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 (2 - 5)^2 = (-3)^2 = 9 && (5 - 5)^2 = 0^2 = 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 (4 - 5)^2 = (-1)^2 = 1 && (5 - 5)^2 = 0^2 = 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 (4 - 5)^2 = (-1)^2 = 1 && (7 - 5)^2 = 2^2 = 4 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 (4 - 5)^2 = (-1)^2 = 1 && (9 - 5)^2 = 4^2 = 16. \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{array}</math>E tu'u atu lelei, ia a'oa'oina le tu'ugamalu o le tulaga uma mai le mea, ma fa'ate'a atu le tu'ugamalu o le tulaga uma mai le mea i le pito ma le result o lea:<math display=\"block\">\\sigma^2 = \\frac{9 + 1 + 1 + 1 + 0 + 0 + 4 + 16}{8} = \\frac{32}{8} = 4.</math>O le variensa e le o le mea o nei valu:<math display=\"block\">\\sigma = \\sqrt{ 4 } </ins>= <ins class=\"diffchange diffchange-inline\">2.</math>ma o le fa'agaioiga o le populasi e tasi leaga ai le square root o le variensa:<math display</ins>=<ins class=\"diffchange diffchange-inline\">\"block\"> \\mu \\equiv \\operatorname{E}[X] </ins>= <ins class=\"diffchange diffchange-inline\">\\int_{-\\infty}^{+\\infty} x f(x) \\, \\mathrm dx </math>E fa'amaopoopo lava le fa'atonutonu lenei i le taimi lava e tu'u atu ai i ai maualuga valu na aloa'i ai lelei le naunauta. Afai o le manatu na aloa'i i ai, o se la'auiloa e filifili mai le tagata e i ai lea malamalama (ma fa'apea foi, o lo'o iai 8 tagata e filifilia atu mai se kosi matutua o le 2 miliona), ona o lea, o lea e aofia ai i le 7 (o le n - 1) i le totonu o le lauelee na, ae le 8 (o le n) o le totonu o le fa'afitauli muamua, ma o le tulaga o lelei o lea e s </ins>= <ins class=\"diffchange diffchange-inline\">32/7 \u2248 2.1.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I lea taimi, o le tulaga o le fa'afitauli asiasia o le muamua o le lauelee o lea e tapunia ai le saini fa'atupu ma fa'amauina i le saini fa'atupu o lea e sainia ai le \u03c3. O le fa'atonuina o le n - 1 i se taimi e le n e fa'afitaulia ai le saini fa'atupu, e solosolo fa'atino ai le tu maualuga o le fa'atupu o le kosi matutua. O lenei lea o le Bessel's correction. Fa'apea ai ma le tupe na feso'ota'i ai i ai, o le lelei o lea ona o le fa'afitauli o le kosi matutua, o lea ua fa'atino i ai le fa'afitauli e fa'amauina i le fa'afitauli o lea naunauta.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fua'iga masani o le maualuga maualuga mo alii matutua ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math display=\"block\"> \\sigma \\equiv \\sqrt{\\operatorname E\\left[(X - \\mu)^2\\right]} = \\sqrt{ \\int_{-\\infty}^{+\\infty} (x-\\mu)^2 f(x) \\, \\mathrm dx }, </math>Pe afai e avea le lauelee o le i'uga i le nu'u o lo'o teuteuina ai, o le fa'atupu o le saini fa'atupu e fa'atagaina ai le malosi o tagata i luga ma i lalo o isi vaega o le nu'u. Mo le fa'amatalaina, o le tele o le taumafataga o tagata ta'itasi i le United States, o le a avea ma le 70 inisi, ma le saini fa'atupu e 3 inisi. O lea na fai mai e fa'apea, o le taumafataga o tagata e le uma lelei (e le'i aofia e 68%, pe a iloilo fa'atasi ai le fa'atupu o le saini e mafai ona vave) e i ai se taumafa inisi i totonu o 3 inisi mai le malosi (67\u201373 inisi) - se saini fa'atupu tuai ona - ma ia le'i aofia ni tagata (e le'i aofia e 95%) e i ai se taumafa inisi i totonu o 6 inisi mai le malosi (64\u201376 inisi) - lua saini fa'atupu. Afai o le saini fa'atupu e leai se mea, ona o ni tagata uma e le'i aofia ni 70 inisi. Afai o le saini fa'atupu e 20 inisi, ona o le aofia o ni tagata e le'i leaga tagata, ma se tau o ni tagata e malosi atu e avea ma le 50\u201390 inisi. O lua saini fa'atupu e alu i le 99.73% o le nu'u o le fa'atupu sa'ilua, pe a filifili mai le fa'atupu o lea e iloilo ai e le o se vaega (vaega) vaega (68\u201395\u201399.7) po'o le tulaga o le naunauta, mo nisi fa'amatalaga.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Fa'amatalaga o tau o tagata ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ia \u03bc le tau e fa'apea (le malosi) o le tautua vaivai X ma le tofa f(x):<math display=\"block\">\\sigma = \\sqrt{\\frac{1}{N} \\left</ins>[<ins class=\"diffchange diffchange-inline\">(x_1 - \\mu)^2 + (x_2 - \\mu)^2 + \\cdots + (x_N - \\mu)^2\\right]},\\text{ where } \\mu = \\frac{1}{N} (x_1 + \\cdots + x_N),</math>O le fa'atupu o le saini \u03c3 o X na fa'amatala</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">\\sigma = \\sqrt{\\frac{1}{N} \\sum_{i=1}^N (x_i - \\mu)^2},\\text{ where } \\mu = \\frac{1}{N} \\sum_{i=1}^N x_i.<</ins>/<ins class=\"diffchange diffchange-inline\">math>lea e mafai ona faaalia e tutusa <math display=\"inline\"> \\sqrt{\\operatorname E\\left[X^2\\right] - (\\operatorname E[X])^2}.<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E mafai ona toe tusa ai le saini fa'atupu i le va o le toso o le mea ua tu\u02bbufa\u02bbatasiga ai le a se mafaufau aofaiga ma le saini o le mea ua tu\u02bbufa\u02bbatasiga:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le fa'atupu o le saini mo se fa'atupu o le auina o le faleupolu o se tautua e le o le mea e pei ona leai se vaega o se tautua e i ai</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E le o se mea uma lava na o le mea e pei ona leai se saini fa'atupu i nisi o vaega vaivai. Afai o le faleupolu na i ai tupe tu'ufa'atasiga e o atu i le isi, e leai se saini fa'atupu, ona o le leaga o le vaega e leai se fa'aiuga. O le faleupolu normal na o le tala e o atu i le isi, ae o le \u03bc ma le \u03c3 na tu'i, ona o le tala na aga'i aunoa mai i luga. O le faleupolu Pareto ma le paramita \ud835\udefc \u2208 (1, 2] e na o le tala, ae leai se saini fa'atupu (pe a tapunia, o le saini fa'atupu o lea e leaga). O le faleupolu Cauchy e leai se tala po'o se saini fa'atupu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'asolo fa'afuase'i ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le taimi o le X na maua ai nisi valu mai le suafa tu'ufa'atasiga x1, x2, ... x1, x2, ..., ma ia valu na i ai le mea e leai ni tupe i ai, o le fa'atupu o le saini na naunau.<math display=\"block\">\\sigma = \\sqrt{\\sum_{i=1}^N p_i(x_i - \\mu)^2},\\text{ where } \\mu = \\sum_{i=1}^N p_i x_i.</math>pe a fa'aaoga le su'ega,<math display=\"block\">\\sigma = \\sqrt{\\int_\\mathbf{X} (x - \\mu)^2\\, p(x)\\, \\mathrm dx},\\text{ where } \\mu = \\int_\\mathbf{X} x\\, p(x)\\, \\mathrm dx,</math>pe a leai se fa'atumauina o ni tau i luga, e maua ai ni tau fa'apitoa, ia x1 e maua ai le tau p1, ia x2 e maua ai le tau p2, ... p2, ... e maua ai le tau pN. I lea taimi, o le fa'atupu o le saini e fa'aaog\u0101 ai lea tau:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''\u03c3''=''p''1\u200b(''x''1\u200b\u2212''\u03bc'')2+''p''2\u200b(''x''2\u200b\u2212''\u03bc'')2+\u2026+''pN''\u200b(''xN''\u200b\u2212''\u03bc'')2\u200b</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O lea na fa'atuina i luga o le tu'uga taua</ins>.<ins class=\"diffchange diffchange-inline\"><math display=\"block\">s_N = \\sqrt{\\frac{1}{N} \\sum_{i=1}^N \\left(x_i - \\bar{x}\\right)^2},<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fesuia'i fa'asolosolo fa'asolosolo ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E leai se saini fa'atupu i se vaega o se vaivai vaivai o le tau tu'ufa'atasiga X e aofia ai le fa'atupu o le tau.<math display=\"block\">s^2 = \\frac{1}{N - 1} \\sum_{i=1}^N \\left(x_i - \\bar{x}\\right)^2.<</ins>/<ins class=\"diffchange diffchange-inline\">math>ma le feutaga o lenei, o ia o le toonai tu'ufa'atasiga na teuteuina i luga o le a ala atu ai le tau X.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ia le taimi o se aiga o tautua tu'ufa'atasiga, e mafai ona fa'aaog\u0101 le fa'atupu o le saini ma ni saini. Mo se fa'atupu, i le taimi o le faleupolu loga-naunau ma paramita \u03bc ma \u03c32, o le fa'atupu o le saini e fa'apea ai</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">s = \\sqrt{\\frac{1}{N-1} \\sum_{i=1}^N \\left(x_i - \\bar{x}\\right)^2}.<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Fa'atatau ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math display=\"block\">c_4(N)\\,=\\,\\sqrt{\\frac{2}{N-1}}\\,\\,\\,\\frac{\\Gamma\\left(\\frac{N}{2}\\right)}{\\Gamma\\left(\\frac{N-1}{2}\\right)}.</math>O se tasi e mafai ona mauaina le fa'atupu o le saini i le nu'u atoa i galuega (e pei o le galuega taua) ma se ituaiga o le nu'u na filifilia. I galuega ma galuega e le mafai ona faia ai lenei, o le fa'atupu o le saini \u03c3 e fai mai i le feso'ota'i o se sampulu talafeagai mai le nu'u ma le fa'ateleina o se tusitusiga o le sampulu, lea na fa'aaog\u0101 e fa'aaog\u0101 lea i le fa'amauina o le fa'atupu o le saini o le nu'u. O lea tusitusiga o le sampulu e numera lea o se fa'amau, ma e nonofo i lea tusitusiga (po'o le valu o le tusitusiga, o le a leai se fa'atele) e numera lea o le fa'atupu o le saini o le nu'u. O se tusitusiga e numera lea o se mea fa'atonu, ma o lenei tusitusiga (po'o le tau o le tusitusiga, ua pepelo lea tusitusiga) e numera lea o le fa'atupu o le saini o le nu'u, ma ua to'eseina i le s.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">In\u0101 ia tusa ai le fa\u02bbasoa\u02bboina o le tau o le nu\u02bbu, ina ia maua ai le nu\u02bbu tau, o le nu\u02bbu tau o le sampulu o se fa\u02bbatulaga e fa\u02bbaogaina ai ni agava\u02bba e le\u02bbo ta\u02bbuta\u02bbua (e leai ni se galuega, leaga, le pito i le auala lea o le agava\u02bba). E leai se tusitusiga tauni e fa\u02bbatupula\u02bbia mo le fa\u02bbatupu o le saini ma i ai nei agava\u02bba uma, ma o le fa\u02bbatupu o le saini e le mafai ona mauaina uma o nei agava\u02bba, ma o le fa\u02bbaaog\u0101 o le fa\u02bbatupu o le saini o le nu\u02bbu o se galuega fa\u02bbaaoga atu e le o ni feso\u02bbotaiga e le\u02bbo faia ai nei tusitusiga. Fa\u02bbaaoga atu i le mafua\u02bbaga lea o le saini, o le fa\u02bbatupu o le saini e mafai ona mauaina ma le fa\u02bbamauina o le fa\u02bbatupu o le saini o le sampulu (fa\u02bbaaoga atu i le N - 1), na tusia i lalo, ma o lea na toe fa\u02bbamauina e fa\u02bbaaog\u0101 i le ituaiga \"fa\u02bbatupu o le saini o le sampulu\", i le vaega nei. O lea tu\u02bbuina atu i so\u02bbo se tusitusiga ma lelei i isi mea</ins>: <ins class=\"diffchange diffchange-inline\">o le tusitusiga le\u02bbo tatalaina (fa\u02bbaaoga atu i le N) na fa\u02bbaaoga e maua ai le su\u02bbesu\u02bbega ma le tapenapena lata (e leai se nofoaga, e leai leaga, e leai ni mea e leaga). e \u02bbavea ai le N - 1.5 (mo le nu\u02bbu o lo\u02bbo tu\u02bbuina) na le fa\u02bbauuina loa le fa\u02bbamoemoe.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'ata'ita'iga e le'i fa'asa'oina le fa'asologa masani ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le fa'atupu mo le saini fa'atupu o le nu'u (o se nu'u taua) e mafai ona fa'aaog\u0101 i le sampulu, e fa'aaog\u0101 ai le sae o le sampulu e le gata o le sae o le nu'u (ae o le malamalama o le sae o le nu'u e taua i lea na teuteuina le sampulu), e to'a iga i ai lea tusitusiga, o le sN, na taunuu ai lea e leai se fa'ateleina i le fa'atupu o le saini o le sampulu (ua fiafia lea fa'atupu o le saini o le sampulu e taua i le nu'u atoa), ma na tusia ai i lalo:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''sN''\u200b=''N''1\u200b\u2211''i''=1''N''\u200b(''xi''\u200b\u2212''x''\u02c9)2\u200b</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I lenei tusitusiga, ''N'' ua ta'uta'uina i le sae o le nu'u o le sampulu, ''xi''\u200b ua faia ai le tu'uta'uina o le m\u0101nea, ma ''x''\u02c9 na faia ai le fa'atupu o le m\u0101nea o le sampulu.<math display=\"block\">\\hat\\sigma = \\sqrt{\\frac{1}{N - 1.5} \\sum_{i=1}^N \\left(x_i - \\bar{x}\\right)^2},</math>Ma le taitaifono, { \ud835\udc65 1 , \ud835\udc65 2 , \u2026 , \ud835\udc65 \ud835\udc41 } o nei tusitusiga, ma \ud835\udc65 \u00af na faia ai le m\u0101nea o lenei mau mana'o, ae o le denominator N na maua ai le sae o le sampulu: o le ulufale o le fa'atupu o le saini o le sampulu, na tusia i lalo, o le a o lona tu'utu'uga na faia ai le fa'atupu o le m\u0101nea o le sampulu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''sN''\u200b=''N''1\u200b\u2211''i''=1''N''\u200b(''xi''\u200b\u2212''x''\u02c9)2\u200b</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I lenei tusitusiga, ''N'' ua ta'uta'uina i le sae o le nu'u o le sampulu, ''xi''\u200b ua faia ai le tu'uta'uina o le m\u0101nea, ma ''x''\u02c9 na faia ai le fa'atupu o le m\u0101nea o le sampulu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O lea tusitusiga na fa\u02bbatino ina ia ona toe foa\u02bbi i le tau o le nu\u02bbu e ao ina ia mulimulita\u02bbi le numera o samupulu e o i ai le sampulu, ma o le fa\u02bbatupu o le saini i le a\u02bbafia lea o le sae o le sampulu o le m\u0101nea. E le\u02bbo ta\u02bbuta\u02bbua mo le mea lea ona na taua i luga, ma o le tusitusiga fa\u02bbatino lenei i le mea na fesiligia i lea o le nu\u02bbu na tu\u02bbuina i le normali distribution. A\u02bbo ia na tusia e, o le tusitusiga lenei na leaga, ona o le aumaia lelei o na tusitusiga ua fa\u02bbapenitia i ni agava\u02bba, o le atamai o le leaga e leaga i le sae o le sampulu, e mama\u02bbi atu ai lea i le faafofoga o 1/N, ma o lea tu\u02bbuina atu i lea tusitusiga i totonu o ni sae vaivai pe vaevae; mo ''N''>75, ua ma\u02bbea ona leaga o le mea e leai se 1%. Ma ni sae vaivai e tele, o le saini fa\u02bbatupu o le sampulu lea na fa\u02bbapenei i ni tusitusiga ua fa\u02bbapenitia.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'asa'o fa'ata'ita'iga sese fa'ata'atia ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Afai o le tusitusiga ua leaga (o le alua fa'atupu i le leaga, o se tusitusiga leaga o le nu'u tau), o le a fa'aaog\u0101 i le fa'atupu o le saini o le nu'u, le fa'atupu o le saini o le nu'u e maua ai o lea:<math display=\"block\">\\hat\\sigma = \\sqrt{\\frac{1}{N - 1.5 - \\frac{1}{4}\\gamma_2} \\sum_{i=1}^N \\left(x_i - \\bar{x}\\right)^2},</math>Ia o le fa'atupu o le onosa'i matua, e le mafai ona fa'aaog\u0101 le fa'atupu o le saini o le nu'u, ona o le mata'utia o Jensen, ona o le fa'atupu o le onosa'i matua e leai se galuega. O le leaga i le fa'atupu o le nu'u e mafai ona fa'aaog\u0101 ai, ae o le leaga mai le onosa'i matua e leaga ona o le matamata o le fa'atupu o le nu'u, ma e mafai ona fa'amauina ai, ae o le leaga o le onosa'i matua e leaga e leai se fa'agaioiga e fa'atino i ai, ma e fa'atino i le fa'atupu o le nu'u.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se tusitusiga e le leaga mo le fa'atupu o le nu'u o le leaga, e mafai ona fa'aaog\u0101 i le fa'atupu o le nu'u o le leaga o le nu'u o le sampulu, o le a tusia i lalo o Bessel's correction, fa'aaog\u0101 atu i le N - 1 i le a fa'aaog\u0101 ai le fa'atupu o le nu'u o le leaga e leaga mo le fa'atupu o le nu'u, o le tusitusiga o le fa'atupu o le nu'u o le leaga, na tusia i lalo, o le s2:<math display=\"block\">\\Pr\\left(q_\\frac{\\alpha}{2} < k \\frac{s^2}{\\sigma^2} < q_{1 - \\frac{\\alpha}{2}}\\right) = 1 - \\alpha,</math>O le tusitusiga lenei e le leaga pe le leaga o le nu'u ma e fa'atino i ai lea tusitusiga ma le galuega e uiga i le nu'u taua taua. O N - 1 e fa'apea ai le numera o le nu'u e fa'atino ai le fa'atupu o le nu'u o le leaga, e pei o le tusitusiga o le nu'u taua, o (\ud835\udc65\u2081\u2212\ud835\udc65\u0304, \u2026, \ud835\udc65\u2099\u2212\ud835\udc65\u0304).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ia o le fa'atupu o le onosa'i matua, e le mafai ona fa'aaog\u0101 le fa'atupu o le nu'u, ona o le mata'utia o le onosa'i matua e leaga ona o le galuega, (o le tasi leaga, o le onosa'i matua e le fa'agaioiga i le fa'atupu o le nu'u, ua leai ona mana'o). O le fa'atupu o le saini fa'atupu o le sampulu na fa'aaog\u0101, na tusia i lalo, o le s:<math display=\"block\">\\Pr\\left(k\\frac{s^2}{q_{1 - \\frac{\\alpha}{2}}} < \\sigma^2 < k\\frac{s^2}{q_{\\frac{\\alpha}{2}}}\\right) = 1 - \\alpha.</math>E fa'apefea i luga, na tusia i luga, peita'i o le s2 o se tusitusiga e le leaga i le fa'atupu o le nu'u o le leaga, ae le o le s o se tusitusiga e le leaga i le fa'atupu o le nu'u o le leaga, ae leaga e leai leaga i le fa'amauina o le s2. O le tusitusiga lenei e fa'aaog\u0101 atu ma o le tusitusiga ua mafai ona iloilo atu i ai pe na o le tusitusiga ua tusia i luga, o le tusitusiga ua fa'aaog\u0101 i ai, ma ua malamalama ai loa i le \"saini fa'atupu o le sampulu\". O le leaga e leaga o lea, o le tata leaga mo nei sampulu (N lagona le 10) e mafai ona sili atu ai lea. A fa'aaloalo i lea, e le o le fa'apefea le leaga, e sili le leaga ma le sae o le nu'u, o le sae leaga peita'i e leai leaga. O lea e maua i ai ni fa'amatalaga ma le se mea na fa'aaog\u0101 ai ma le tautua i le galuega.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'ata'ita'iga l\u0113 fa'aituau fa'aa'oa'oga fa'a'ese'ese ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo le fa'amaoniga e le leaga mo le fa'atupu o le saini fa'atupu o le nu'u, e leai se fomula e mafai ona fa'aaog\u0101 i le vaiaso uma, peita'i mo le m\u0101nea ma le leaga. Atonu o le s, e fa'aaog\u0101 atu e le fa'aaog\u0101, ma e taele i se fakt\u014d o le fa'atupu e fa'atino le leaga. I le nu'u normali, o se tusitusiga e leaga ai o lo'o fa'apea ai le s/c4, ma o lea e sili atu ai i le t\u014dlua o le fa'atupu (o lea e mafai ona tautuaina ai e N) ua i ai le fa'atino i le tu'utu'uga o le Gamma, ma e galulue i ai:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''c''4\u200b=''N''\u221212\u200b\u200b\u22c5\u0393(2''N''\u22122\u200b)\u0393(2''N''\u22121\u200b)\u200b</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I lenei, \u0393(''x'') na fa'aaog\u0101 mo le gamma function. O le fakt\u014d fa'atino leaga lenei o le saini fa'atupu o le sampulu ina ia fa'atino ai le leaga o le nu'u o le saini fa'atupu.<math display=\"block\">s(X) = \\sqrt{\\frac{N}{N-1}} \\sqrt{\\operatorname E\\left[(X - \\operatorname E[X])^2\\right</ins>]<ins class=\"diffchange diffchange-inline\">}.</math>O lea na mafai ai ona ala i le feso'ota'iga taua o le saini fa'atupu o le sampulu, ua mafai ona faia i se distribution chi (fa'atino) ma o le fakt\u014d fa'atino leaga na fa'atino ai le tu'utu'uga o le chi distribution.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se malamalama e mafai ona tuuina atu e pei ona fa'alauiloaina le N - 1 i le N - 1.5, ma o lea e maua ai:<math display=\"block\"></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\sqrt{\\frac{1}{N}\\sum_{i=1}^N\\left(x_i - \\bar{x}\\right)^2} =</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\sqrt{\\frac{1}{N}\\left(\\sum_{i=1}^N x_i^2\\right) - {\\bar{x}}^2} =</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\sqrt{\\left(\\frac{1}{N}\\sum_{i=1}^N x_i^2\\right) - \\left(\\frac{1}{N} \\sum_{i=1}^{N} x_i\\right)^2},</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"></math>O le leaga i lenei malamalama o le tusitusiga na fa'alauiloa ai, ua solosolo leaga (e leai ni tolu), ma e tata lea i ni sampulu, po'o le matamata o le malosi: mo N = 3, o le leaga e 1.3%, ma mo N = 9, o le leaga e leai ni 0.1%.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se malamalama e mafai ona tuuina atu e pei ona fa'alauiloaina le N - 1.5 i luga o le N - 1.5 + 1/8(N - 1), ma o lea e maua ai:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo isi nu'u taua, o le fomula e tatau ona fa'atumauina i le nu'u taua, ae o se uo lea e fa'aaoga ai le fa'alauiloaina o le malamalama:<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \\sigma(c) &= 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\sigma(X + c) &= \\sigma(X), \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \\sigma(cX) &= |c| \\sigma(X).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>I lea na t\u0101l\u0101 ai le \u03b32 na tusia ai le nu'u o le nu'u tau, na mafai ona iloilo ai le \u03b32 mai le tatau taua pe o lo'o ia mafai ona iloilo mai le data.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Vava fa'atuatuaina o se fa'ata'ita'iga fa'ata'ita'iga sese ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le fa'atupu o le saini fa'atupu o le sampulu na faia ai, e leai se mea e taua ai, ona o galuega matematika (ua fa'ailoilo i lenei i luga o le confidence interval) ma galuega o le mafaufau (mefa\u02bba\u02bbai i tupe o le l\u0101). O le au\u0101le\u0101li\u02bbi o le mea matematika e mafai ona fa\u02bbailoilo i le fa\u02bbagaluega o le confidence interval, pe CI.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo le fa\u02bbasa\u02bbolotoina o le a se sampulu e m\u0101toa ai ona ia l\u0113tatau le confidence interval, fa\u02bbaaoga ai ni faamaumauga o lo\u02bbo taua:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se nu\u02bbu itiiti e ''N''=2, e leai ni sae mo le fa\u02bbatupu o le saini fa\u02bbatupu o le sampulu. O lea na maua ai se 95% CI o le SD mai le 0.45\u00d7''SD'' i le 31.9\u00d7''SD''. O lea ni fa\u02bbato\u02bbaga o le mea na fa\u02bbaaog\u0101:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">0.45=1\u22124(2\u22121)2\u200b\u200b 31.9=2(2\u22122)2(22\u22121)\u200b\u200b</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O ni fa\u02bbatoaga fa\u02bbaleaganuu o le lautele ma le sae o le nu\u02bbu o le saini fa\u02bbatupu o le sampulu.<math display=\"block\"> \\sigma(X + Y) = \\sqrt{\\operatorname{var}(X) + \\operatorname{var}(Y) + 2 \\,\\operatorname{cov}(X,Y)}. \\, </math>Ua fa\u02bbailoilo mai lenei, ''qp''\u200b e sili atu ai i le p-th quantile o le distribution chi-square ma k degrees of freedom, ma 1 - \u03b1 e le galuega o le tu\u02bbufa\u02bbatasiga. O lea e amatalia pe a sili lea i le: ''q''2''\u03b1''\u200b,''k''\u200b ma le: ''q''1\u22122''\u03b1''\u200b,''k''\u200b Toa\u02bbaga sa fai mai le distributi i luga o le tasi.<math display=\"block\">\\sigma(X) = \\sqrt{\\operatorname E\\left[(X - \\operatorname E[X])^2\\right]} = \\sqrt{\\operatorname E\\left[X^2\\right] - (\\operatorname E</ins>[<ins class=\"diffchange diffchange-inline\">X])^2}.</math>Ma k = 1, o le q_{0.025} = 0.000982 ma le q_{0.975} = 5.024. O le reciprocals o le a aga'i o i latou nei na maua ai o ni factors e 0.45 ma 31.9 na taua i luga.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Ua ia fa\u02bbamauma e lea lenei o le lagona o le a se nu\u02bbu le\u02bbi tatau i le ''N''=10 na tu\u02bbufa\u02bbatasiga ai i le saini fa\u02bbatupu o le sampulu. Ua maua ai lea ni tala e pei ona tu\u02bbufa\u02bbatasigaina i luga o le a launia</ins>:</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Aso 95% CI o le SD o le 0.69\u00d7''SD'' i le 1.83\u00d7''SD''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* E tusa ai ma le ''N''=10, o le a mafai ona lea e le 2 ni le saini fa\u02bbatupu o le sampulu. Mo le sample population ''N''=100, o lea ua tatau ona leaga lea i le 0.88\u00d7''SD'' i le 1.16\u00d7''SD''. E tatau lava ona fa\u02bbamauma lea le SD o le sampulu ina ia mafai ona ia ia l\u0113tatau i le SD o le nu\u02bbu o le saini fa\u02bbatupu. Ua tatau ona fa\u02bbamauma lea lea lea i le tautaiga o le a se tasi fa\u02bbata\u02bbita\u02bbiga.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E mafai ona fa\u02bbaaog\u0101 ai foi nei fomula e l\u0113tatau le confidence interval o le variance o le a se tomai mea'ai mai le vaega o le a se ese\u02bbese o le vaega ese\u02bbese o le lagona, i le mafai ai le m\u0101nea o k e fai ma le numera o sae o le ala.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'amauina i le fa'asologa masani ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo se seti o data e lagolagoina ai ni numer\u0101 N > 4 ma se tulaga R, o le se\u02bbia aafia ai lea o le saini fa\u02bbatupu o le sampulu o le R = 0.6. O se tusitusiga o le saini fa\u02bbatupu mo N > 100 o se vaega o data lagona i le talu ai o le mafai ona ia sili i se vaega ese\u02bbese, ma e taua le m\u0101nea e fa\u02bbaaog\u0101 ai lenei o le gagana e fa\u02bbaalia ai le 95% o le su\u02bbesu\u02bbe i luga o le fale normali ua l\u0113toa lea i ni saini fa\u02bbatupu ua i ai se 2 saini fa\u02bbatupu i luga o le maualuga ma le maualalo o le m\u0113ana, ma o lea ua tu\u02bbufa\u02bbatasiga ai i luga o le 95% a\u02bboga le tulaga o le R e fa\u02bbatusatusa ai le four saini fa\u02bbatupu ina ia saini \u2248 R</ins>/<ins class=\"diffchange diffchange-inline\">4. O le malamalama lea i luga o le a leaga atu le Range Rule, e mafai ona fa\u02bbamaut\u016bina i le avanoa o le sampulu, ona o lea e l\u0113l\u0101oina ai le saini fa\u02bbatupu. O ni isi foafoa N (K(N)) o le range e fa\u02bbaaog\u0101 i le saini fa\u02bbatupu e fa\u02bbaali ai le R</ins>/<ins class=\"diffchange diffchange-inline\">K(N) mo isi tulaga o N ma isi nu\u02bbu taua e le normali</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Fa'ailoga ma uiga fa'a-matematika ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le saini fa'atupu o le sampulu e le leaga i le fa'atauina o le nofoaga, ma e fa'atau atu i le fa'atau o le mata'upu taua</ins>. <ins class=\"diffchange diffchange-inline\">O lea ua ia feso'ota'i ai, mo se tau constat c ma mata'upu taua X ma Y:<math display=\"block\">M = \\left(\\bar{x}, \\bar{x}, \\bar{x}\\right)<</ins>/<ins class=\"diffchange diffchange-inline\">math>O le saini fa'atupu o le mamalu o le lua mata'upu taua e mafai ona fa'amaut\u016b i le aofaiga o le saini fa'atupu o ia mata'upu taua ma le covariance i loto ia te ia:{{Collapse top|title=Derivation of <math>M = \\left(\\bar{x}, \\bar{x}, \\bar{x}\\right)<</ins>/<ins class=\"diffchange diffchange-inline\">math>}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math>M</math> is on <math>L</math> therefore <math>M = (\\ell,\\ell,\\ell)</math> for some <math>\\ell \\in \\mathbb{R}<</ins>/<ins class=\"diffchange diffchange-inline\">math>.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">The line {{mvar|L}} is to be orthogonal to the vector from {{mvar|M}} to {{mvar|P}}. Therefore</ins>:</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"><math display=\"block\">\\begin{align} </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 L \\cdot (P - M) &= 0\u00a0 \u00a0 \\\\[4pt</ins>]</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 (r, r, r) \\cdot (x_1 - \\ell, x_2 - \\ell, x_3 - \\ell) &= 0\u00a0 \u00a0 \\\\[4pt]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r(x_1 - \\ell + x_2 - \\ell + x_3 - \\ell) &= 0\u00a0 \u00a0 \\\\[4pt]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r\\left(\\sum_i x_i - 3\\ell\\right) &= 0\u00a0 \u00a0 \\\\[4pt]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\sum_i x_i - 3\\ell &= 0\u00a0 \u00a0 \\\\[4pt]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\frac{1}{3}\\sum_i x_i &= \\ell \\\\</ins>[<ins class=\"diffchange diffchange-inline\">4pt]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\bar{x} &= \\ell</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{Collapse bottom}}ua var=''\u03c3''2 ma cov ua tofia le variance ma le covariance, fa'aaoga atu i ai.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le tusitusiga o le mamalu o le sumi o le malosi fa'atupu e mafai ona fa'amaut\u016b i lenei tua ia taua e lua na tusia i luga o le data. I le fomula lalo, o le itulagi E e iloilo i lenei e tatau ona fa'amaonia le mafai o lenei mea, lea o le mea o le m\u0101nea.<math display=\"block\">f\\left(x, \\mu, \\sigma^2\\right) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}\\left(\\frac{x - \\mu}{\\sigma}\\right)^2}</math>O le saini fa'atupu o le sampulu e mafai ona tusia pe fa'amaut\u016b ai</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">\\text{Proportion} = \\operatorname{erf}\\left(\\frac{z}{\\sqrt{2}}\\right)<</ins>/<ins class=\"diffchange diffchange-inline\">math>Mo se nu'u taua e leaga i ai ni mafuaaga o le fa'amaut\u016b o le fa'atupu o le sampulu, o le a saunoa pe:<math display=\"block\">\\text{Proportion} \\le x = \\frac{1}{2}\\left[1 + \\operatorname{erf}\\left(\\frac{x - \\mu}{\\sigma\\sqrt{2}}\\right)\\right] = \\frac{1}{2}\\left[1 + \\operatorname{erf}\\left(\\frac{z}{\\sqrt{2}}\\right)\\right].<</ins>/<ins class=\"diffchange diffchange-inline\">math>O le uiga o le fa\u02bbasalaga mo le malosi fa\u02bbatupu o se seti o ni tulaga e fa\u02bbaaoga i le tofa, o le faia lea e tatau ona tatalo ai pe o lea e tele i ai se fa\u02bbamaut\u016bina (maea).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fa\u02bbamolemole, tilotilo i le fomula o le taua mo le saini fa\u02bbatupu e fa\u02bbailoilo, ma mo se tu\u02bbuina o le saini fa\u02bbatupu o le sampulu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Faamatalaina ma le faaaogaina ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Comparison_standard_deviations.svg|right|thumb|400x400px| Fa\u02bbamatalaga o ni sampulu mai lua nu\u02bbu taua e i ai le maea, ae ua leaga le saini fa\u02bbatupu. O le nu\u02bbu pula o le mean 100 ma le SD 10; o le nu\u02bbu lanu moana o le mean 100 ma le SD 50.]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le saini fa\u02bbatupu tele o se fa\u02bbatut\u016b e fa\u02bbailoilo ai e le o mafai ona ia vaelua atu i le maea, ma o se saini fa\u02bbatupu li\u02bbiti o le fa\u02bbailoilo ai ua tele i ai i luga o le maea.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo se fa\u02bbamatalaga, ua mafai ona fai ni nu\u02bbu e lua e pei o le {0, 0, 14, 14}, {0, 6, 8, 14} ma {6, 6, 8, 8} e i ai le mean o le 7. O lenei o lo\u02bbo i ai se maea o 7, 5, ma 1 ona lenei. O le nu\u02bbu e tolu na i ai se saini fa\u02bbatupu e le tele ona le lua na lenei, ona o ni vaega o le nu\u02bbu e lagona atu i le 7. O lenei saini fa\u02bbatupu e tusa ai ma le vaega o le nu\u02bbu taua na faia. Pe, mo se fa\u02bbaauauina, o le seti o le data {0, 6, 8, 14} e fa\u02bbalagolago i ai ni taimi a le toa o lona totonu i le nu\u02bbu taua na faia, o lea ua maea o le 5 tausaga. Mo se tusa o se fa\u02bbamatalaga, o le nu\u02bbu taua {1000, 1006, 1008, 1014} na faia e tusa ai ma ni fetau, ua tusia i le mita. O lea e maea o le mean 1007 mita, ma saini fa\u02bbatupu o 5 mita.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le saini fa'atupu o se mea e mafai ona fa'aaog\u0101 e avea ai ma le fefe. I le tama'ita'i fizikasi, mo se fa\u02bbamatalaga, o le saini fa\u02bbatupu ua tukuina mai i luga o se tausaga o ni maea o tulaga o le fa\u02bbamauina o nisi tu\u02bbuina. I le taimi e filifilia ai pe o lea e mafai ona tu\u02bbufa\u02bbatasiga ai ni maea i le tala sa tala, o le saini fa\u02bbatupu o ia maea o se mea fa\u02bbaaoga e leaga ai: pe o le mean o le maea e l\u0113 lagona atu i le fa\u02bbasalaga (ma le distanse e fa\u02bbasalaga ai i le saini fa\u02bbatupu), ona o le leaga ua aofia ma le fa\u02bbamaut\u016b o le tala, o le mea e filifilia ona suia ai le tautua. E tusa ai lea pe, i le taimi e filifilia ai pe o lea e lagona atu i luma o se tala l\u0113 masani, o le saini fa\u02bbatupu o ia tala e mafai ai ona tu\u02bbufa\u02bbatasiga i ni maea aofia e fa\u02bbatulagaina: pe o le mean o lenei maea e tolu se'i lagona atu i le tala (ma le distanse ua fa\u02bbasalaga i le saini fa\u02bbatupu), ona o le leaga ua talafeagai i le tala e tala, o le teoria sa t\u0101l\u0101 sa tala pe ua l\u0113 malosi. O lea ua mautinoa, ona o lenei ua teena ni solitulafono ua mautinoa, pe ua l\u0113 masani le mea ua faia, ma o le saini fa\u02bbatupu e fa\u02bbasalaga ai. Silia ma le prediction interval.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">In\u0101 ua m\u0101ta\u02bbutino le saini fa\u02bbatupu e fa\u02bbailoilo i le va o ni maea o fetaui ma le maea, e mafai ona avea ma isi mea. O se fa\u02bbamatalaga lea o le maea o le malosi tu\u02bbufa\u02bbatasiga, sa mafai ona fa\u02bbamaut\u016b e maitauina i le average fa\u02bbamau, ma le leaga i le va o le maea o le malosi fa\u02bbatupu ua tofia i le saini fa\u02bbatupu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'ata'ita'iga fa'atatau ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Fa'ata'ita'iga, su'esu'ega fa'apisinisi ma le fa'atatau ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le saini fa\u02bbatupu o lo\u02bbo fa\u02bbaaog\u0101 i le fa\u02bbamaut\u016bina o tulaga mai le lagona ma le fa\u02bbamaut\u016bina o le saini</ins>. <ins class=\"diffchange diffchange-inline\">Mo se fa\u02bbamaut\u016b e faia, o le malosi o ni mea faigaluega e ala i ai e pei o le tau o mea na tupu mai ai le ofisa o le malo</ins>. <ins class=\"diffchange diffchange-inline\">Afai e sese le fa\u02bbamauina o ni mea, o le a tatalo lea i ai o ni faamaut\u016bina e pei o le leaga o le malosi o lo\u02bbo tuai ma le fa\u02bbamaut\u016bina o le saini. Afai e fa\u02bbamaut\u016bina se sefa o ni mea faigaluega, o le malosi fa\u02bbatupu e mafai ona tu\u02bbufa\u02bbatasiga ai ni tau o se fa\u02bbamaut\u016bina e faia (99.9% pe a sau). Afai e tele nisi o le malosi, ona e mafai ona tusia le vaega o le malosi o lo\u02bbo tuai ma le fa\u02bbamaut\u016bina o le saini. Afai o lo\u02bbo tuai i fafo o le vaega na tu\u02bbuina ai, ona e tatalo lea o lo\u02bbo i ai o ni faamaut\u016bina fa\u02bbapea. O ni fa\u02bbamaut\u016bina fa\u02bbamatalaina e pei o lenei na faia, e le o se fa\u02bbamaut\u016bina, o le fa\u02bbamaut\u016bina o le maliu na avanoa ai se malo i le tofiina o tusi paia, ona e tele se fa\u02bbamaut\u016bina e faia e le malo.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le gagana o le gagana fa\u02bbamaut\u016b, o lea e fa\u02bbaaog\u0101 ai se teoria ua tuai. O le si\u02bbi lava na tusiina e le gagana malosi i le \"5 sigma\" mo le fa\u02bbamoemoe o se vaega e pei o le ata. O le a si\u02bbi sigma na fa\u02bbatautauina e tasi i le 3.5 miliona, o le mafua\u02bbaga na tali i ai le sili e fa\u02bbamoemoe i luma o se faamaut\u016bina e faia. O lenei vaega o le malosi na fesoasoani i le faia o se gaioi e fa\u02bbatonutonu ai le faitau o se partikel o lo\u02bbo fa\u02bbaaoga le Higgs boson, ua amata mai ai fo\u02bbi le faitauina o le fa\u02bbamatalaga fa\u02bbapitoa o le vevela gravet\u0101sione.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Tau ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I se fa\u02bbamatalaga tusitusi, faia le tausiga o le malosi fa\u02bbatupu mo le malosi malosi a le vaega e lua, e tasi i loko ma e lua i le itu tau. Ua fesoasoani ona tatalo e sili le tausaga o le malosi fa\u02bbatupu mo itu malae malae o le itu tau ma o le tino, peita\u02bbi, ina ia avanoa\u02bbi le \u02bbamai\u02bbi itiiti o le tausaga o le malosi fa\u02bbatupu mo itu malae malae mo le itu tau ma o le tino. O lea lava, pe afai e fa\u02bbatulagaina e le malae i tua ma lona malosi fa\u02bbatupu, o le saini fa\u02bbatupu o le malosi fa\u02bbatupu mo le malae malae o le itu tau o lo\u02bbo i ai le itiiti i le malae malae o le itu tau mo le itu tau ma o le tino. I lenei taimi, e mafai ai ona e le\u02bbi totoe le tausaga o le malosi fa\u02bbatupu o le malae malae mo le itu tau o lo\u02bbo i ai le itiiti i le itu tau ma o le tino.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Tupe ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le faletalimalo, o le saini fa\u02bbatupu o lo\u02bbo fa\u02bbaaog\u0101 e tusa ai ma le mea faigaluega e mafai ai ona galue ai i luga o le solitulafono o se m\u0101l\u014d (mea mafai ona valaau, peipi, vaega, etc.), pe o le solitulafono o se pulega o mea faigaluega (fondi mamanu, fondi itulau, po\u02bbo le ETF). O le soifua e se tagata lona tolu le gaioi i le fa\u02bbaaog\u0101 o le solitulafono i m\u0101l\u014d o mea faigaluega, ona o le fa\u02bbaaog\u0101 lea o le solitulafono i mea faigaluega ma o le fondi a mea faigaluega, ma o le ETF. O le soifua o le mea fa\u02bbagaluega e amata mai ai i le fa\u02bbaaog\u0101 o le solitulafono e fale ma lona malosi fa\u02bbatupu i le solitulafono o se tagata. Ua mafai ona avea le soifua i le fa\u02bbamaut\u016bina o le lagona i le tulaga o le avanoa e faigaluega ai i luga o le mea faigaluega ma le po\u02bbo le fondi ma ua mafai ona fa\u02bbaaog\u0101 le gaioi fa\u02bbatupu mo lea mea ma o se matematika fa\u02bbaasease mo le fa\u02bbaoti o le manatu o ni fa\u02bbamoemoe (e i ai le fesilafa i luga o le malaga-vaega). O le uiga o le fa\u02bbamoemoe o se mea gaioi o lea, e aumai ai i ai, o le lagona e fa\u02bbaaog\u0101 ai i le fa\u02bbaaog\u0101 o se mea gaioi o lea, ma ua mafai ona fa\u02bbaaog\u0101 lea i luga o le fa\u02bbamoemoe o le mea gaioi o lea (ua malolosi le fa\u02bbaaog\u0101). I isi ituaiga upu, o le aumai lea ua ia fa\u02bbaliloina ai e le tagata, e mafai ai ona fa\u02bbaoti atu ai se malofie ona lagona i le fa\u02bbaaog\u0101 o se mea gaioi o lea po\u02bbo le tulaga o le mafuaaga. I le taimi e taumafai ai ni fa\u02bbamoemoe, o le aumai lea ua ia iloa ai e le tagata le lagona e fa\u02bbaaog\u0101 ai i le fa\u02bbamoemoe ma le fa\u02bbaaog\u0101 o le malosi o ni fa\u02bbamoemoe lona tekinikolagi. O le saini fa\u02bbatupu o lea o le aumai lea ua ia iloa ai e le tagata le malosi o ni fa\u02bbamoemoe.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Le auina (pe fa\u02bbaaut\u016b) o le fa\u02bbamoemoe o se malolo a ni tulaga e tusa ai ma le \u02bbauala i se taimi e taofio ai le fa\u02bbamoemoe o le m\u0101l\u014d. Mo le auala lava, le fa\u02bbauauina o le fa\u02bbamoemoe mai le fa\u02bbamoemoe o le tupe, o le tulaga ua mautinoa e aofia ai le fa\u02bbamoemoe o le mea faigaluega. Mo le tulaga uma, pei o le fa\u02bbamoemoe o le tupe mai le fa\u02bbamoemoe o le fa\u02bbamoemoe, o le tulaga ua faigofie e maua ai le leaga mai le fa\u02bbamoemoe. Le faia o le fa\u02bbamoemoe i le fa\u02bbamoemoe o le fa\u02bbamoemoe i le tupe o le mea faigaluega. Ua fa\u02bbato\u02bbese le malosi, ua le iloa ma le malosi o le mea faigaluega. Faigofie ona mauaina le manatu o le mea faigaluega ma le malosi o le fa\u02bbamoemoe ma le fa\u02bbamoemoe i le tupe. Le faigofie lea e tauina ai le malosi, o le malosi masani ona tuuina atu ai le gaioi o le fa\u02bbamoemoe. Ua maua ai le fa\u02bbamoemoe ma le fa\u02bbamoemoe o le tupe na fa\u02bbamoemoeina i luga o le gaioi o le malosi o le fa\u02bbamoemoe.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">OO ni tulaga taimi faigaluega na iloa ai e le la\u02bbititi o ni tulaga na fa\u02bbamaut\u016b ai le fa\u02bbamoemoe, ae e le\u02bbi toe fa\u02bbaaut\u016b le mea faigaluega, pe le taitoa e uiga i luga o ni tulaga o le malosi o le fa\u02bbamoemoe. Ina ia amata le fa\u02bbaauau o ni tulaga o le malosi o le fa\u02bbamoemoe i luga o ni tulaga o le malosi o le fa\u02bbamoemoe, o le mea ua mautinoa e toe fa\u02bbaaut\u016b lenei mea faigaluega i se mea faigaluega, ona o le malosi o le fa\u02bbamoemoe ua mautinoa.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fa'amatalaga fa'atusa ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo se iloiloga e fa\u02bbaalia ai ni malamalama fa\u02bbavaivai ma fa\u02bbafitauli, ia mautinoa lea e amata ai i le tulaga o le taua o le tolu, x1, x2, x3. O lea e mautinoa ai se pepa P = (x1, x2, x3) i le R3. Ia talitonu le lalolagi L = {(r, r, r) : r \u2208 R}. O lea o le \"main diagonal\" e ala i le fatu. Pe a o\u02bbe to\u02bbafaitauina ni tulaga o le tolu ua tau, ona o le malosi o le fa\u02bbamoemoe o le P o le 0 ma le P. O lea na tuuina atu i le fatu. E tatau ona ia amatalia le malosi o le fa\u02bbamoemoe ma le fa\u02bbamoemoe o le P. O lea na fa\u02bbafefea ai. Mo le tuai mai i le fatu L i le P, ona amatalia ai mai le pepa:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">e na mafua ai ni malamalama o le fa\u02bbamoemoe ona o se mea masani ona lauina atu ni tulaga o le P i lea ua tuai ma ia.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se fa\u02bbamatalaga itu, na amata e iloa ai le mamao i le P ma M (o lea fo\u02bbi le mamao fa\u02bbatasi i le P ma le lalolagi L) \u2211 \ud835\udc56 ( \ud835\udc65 \ud835\udc56 \u2212 \ud835\udc65 \u00af ) 2 o le mea lea na mafua ai ni malamalama o le fa\u02bbamoemoe o le vaega (x1, x2, x3), ua muamua e le fa\u02bbamoemoe o le m\u0101loa i le f\u0101 o le numera o le vaega (3 i lenei taimi).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Le tutusa o Chebyshev ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">E le masani foi ona mafai ona matou fai ma ni malamalama e masani ma le laitiiti pe afai o se fesiligia taua e aga'i mai le fa\u02bbamoemoe. O le Chebyshev's inequality na fa\u02bbamaonia ai e fa\u02bbato\u02bbese i ai, mo taitai nei i ni tulaga o le malosi o le fa\u02bbamoemoe, le mea e mafai ai ona matou iloa ai le taua o le fa\u02bbamoemoe e tusa ma lea e fa\u02bbamoemoeina i lalo.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{| class=\"wikitable\"</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">!Mamao mai uiga</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">! La'ititi o tagata</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>\\sqrt{2}\\,\\sigma<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 50%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>2\\sigma<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 75%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>3\\sigma</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 89%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>4\\sigma<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 94%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>5\\sigma</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 96%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>6\\sigma</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 97%</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>k\\sigma</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>1 - \\frac{1}{k^2}</math> </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>\\frac{1}{\\sqrt{1 - \\ell}}\\, \\sigma</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>\\ell</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Tulafono mo fa'amaumauga masani fa'asoa ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Standard_deviation_diagram.svg|thumb| O le lanu-moli o le uli ua faatasi ma se malosi o le fa\u02bbamoemoe i le itu e tasi o le fatu. Mo le fa\u02bbamoemoe o lo\u02bbo i luga o le it\u016b taua, o le mea lea e tasi, o le 68.27 faapitoa o le taitai; pe fa\u02bbatasi lea o le malosi o le fa\u02bbamoemoe e lua (uli ma le uli-masani) e aofia ai le 95.45 faapitoa; e aofia ai le 99.73 faapitoa ma le malosi o le fa\u02bbamoemoe e tolu (malamalama, uli ma le uli-masani); ma le aofia ai le 99.994 faapitoa ma le malosi o le fa\u02bbamoemoe e fa (fa, malamalama, uli ma le uli-masani). O lona lua o le au e tolu, ua fa\u02bbapea foi ma le au na\u02bbo se taitai o le malosi o le fa\u02bbamoemoe e tasi mai le fa\u02bbamoemoe.]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le teorema o le malamalama i le uli o le malamalama e na\u02bbo le malosi o ni galuega taua o le malosi, faapitoa mo le faapitoa o ni gaosiga taua e ono leai se taimi, e aofia ai ni tulaga mat\u016b e leai se mea muamua ma e malamalama pea i le uli-masani faapitoa o le malosi ma le galuega taua, na na teena ai le normal distribution e malamalama, ma lea o se pisinisi e leai ni galuega taua.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">lona lima, ia l\u0113 \u016bmalia ai lona lapa, e fesiligia ai le lima o le malamalama o le laititi o le malamalama, pe afai e leai se galuega taua o le malosi. E l\u0113 mafai ai ona ia fa\u02bbailoa i le uiga o le fa\u02bbamoemoe o le galuega taua ma le fa\u02bbamoemoe o le uli-masani, peita\u02bbi ua iloga ai foi i le malamalama ona o le fa\u02bbamoemoe ma le le fa\u02bbamoemoeina.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Pe a i ai ni malosi o le malamalama e amata i le uli-masani, ona mafua ai le taua o ni tulaga taua i totonu o le z standard deviations o le fa\u02bbamoemoe o le galuega taua o le malosi:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">lona m\u0101sani ona o le galuega taua o le malosi. O le taua o ni it\u016b taua e l\u0113 falosaga e tele atu pe tusa ma ni uiga, x, e fa\u02bbapipii i le fuesi o le malamalama:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Pe a i ai ni malosi o le malamalama e amata i le uli</ins>-<ins class=\"diffchange diffchange-inline\">masani, ona mafua ai e le 68 faapitoa o le taua o ni tulaga taua e tolu e i totonu o le taimi (matematika, \u03bc \u00b1 \u03c3, ma le mea e le ai, \u03bc o le galuega taua), ona mafua ai e le 95 faapitoa e tolu e i totonu o le taimi (\u03bc \u00b1 2\u03c3), ma le mea e le ai, le 99.7 faapitoa e tolu e i totonu o le taimi (\u03bc \u00b1 3\u03c3)</ins>. <ins class=\"diffchange diffchange-inline\">O le mea lena o loo i ai le 68\u201395\u201399</ins>.<ins class=\"diffchange diffchange-inline\">7 rule, pe le empirical rule</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo ni tulaga o z, o le malosi o ni gaosiga taua e ta\u02bbu i totonu ma tu\u02bbu i tua o le fa\u02bbamoemoe, CI = (\u2212z\u03c3, z\u03c3), o le aofia ai i lalo:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File:Confidence_interval_by_Standard_deviation.svg|thumb| Pasene i totonu( ''z'' )]</ins>]</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>[<ins class=\"diffchange diffchange-inline\">[File:Standard_deviation_by_Confidence_interval.svg|thumb| ''z'' (Panesene i totonu)]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Tausisi fa\u02bbatau i le fa\u02bbaopoopo ma le fa\u02bbaopoopo ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le mean ma le standard deviation o se seti o datosi o loo faia e le tauva. I se mea lava, o le standard deviation o se maea e fa'amaeaina ai le malosi o le tatou tusi datosi uma uma i le mean. O lea o lea, ona o le standard deviation mai le mean e le uma foi mai ni isi itu. O le faamatalaga e tatau ona iloilo ai, o lea ua faia ai lea</ins>: <ins class=\"diffchange diffchange-inline\">ua ia faia x1, ... x1, ... e masani i tulaga:<math display=\"block\">\\sigma(r) = \\sqrt{\\frac{1}{N - 1} \\sum_{i=1}^N \\left(x_i - r\\right)^2}.<</ins>/<ins class=\"diffchange diffchange-inline\">math>Fa\u02bbaaogaina le kalokula po o le fa\u02bbaopoopo o le ma\u02bbalili, e tatau ona fa\u02bbaalia, o le \u03c3(r) e iai se minimum fa\u02bbaopoopo i le mean:<math display=\"block\">r = \\bar{x}.\\,</math>O le to\u02bbelau o se seti o datosi e tatau ai ona tauva foi i le tusi o le vaega o le to\u02bbelau, o le a ia e tauva ai le standard deviation ma le mean. O se numera e leiloa ai le mamalu o se mea.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fua'iga masani o le uiga ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I totonu, e talafeagai ai ia te outou se fa\u02bbamatalaga i le malosi o le mean ua mafai ona e maua. E mafai ona e maua i lea lava e tautua ai le fa\u02bbamalosi o le sampled mean. Afai e faamaonia le fa\u02bbamaoni o le vaega i le sample, o le fa\u02bbamalosi o le mean o lea e fa\u02bbatatau i le fa\u02bbamalosi o le distribution ma:<math display=\"block\">\\sigma_\\text{mean} = \\frac{1}{\\sqrt{N}}\\sigma</math>I lea lava o le tau, ona o le numera o manatu i le su\u02bbesu\u02bbega e fa\u02bbamauina ai le mataupu. E mafai ona faamatalaina lenei mea i lalo o le (vaavaalua o le mata\u02bbititi):<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\operatorname{var}(X) &\\equiv \\sigma^2_X\\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\operatorname{var}(X_1 + X_2) &\\equiv \\operatorname{var}(X_1) + \\operatorname{var}(X_2)\\\\ </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>O le fa\u02bbamaonia o le taimi fa\u02bba\u02bbaleleia o le lautele.<math display=\"block\">\\operatorname{var}(cX_1) \\equiv c^2\\, \\operatorname{var}(X_1)<</ins>/<ins class=\"diffchange diffchange-inline\">math>ona o le a<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> \\operatorname{var}(\\text{mean})</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 &= \\operatorname{var}\\left(\\frac{1}{N}\\sum_{i=1}^N X_i\\right)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 = \\frac{1}{N^2} \\operatorname{var}\\left(\\sum_{i=1}^N X_i\\right) \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 &= \\frac{1}{N^2} \\sum_{i=1}^N \\operatorname{var}(X_i)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 = \\frac{N}{N^2} \\operatorname{var}(X)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0 = \\frac{1}{N} \\operatorname{var}(X)</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>O le tulaga i:<math display=\"block\">\\sigma_\\text{mean} = \\frac{\\sigma}{\\sqrt{N}}</ins>.<ins class=\"diffchange diffchange-inline\"><</ins>/<ins class=\"diffchange diffchange-inline\">math>I le galuega e fa\u02bbamauina ai le fa\u02bbasaunaina o le malosi masani \u03c3mean, e leai se isi mea e mafai ona iloaina, o le mea ua mautinoa, o le malosi masani o le atunu\u02bbu atoa \u03c3 i le mua. Ae e le\u02bbi iloa i lona fa\u02bbatoa malosi i le polokalama e pei ona galue ai. Mo le fa\u02bbaauauina pea, pe afai e galue ai se tasi o 10 galuega o se ata e leai se iloiloina, e mafai ona amataina le su\u02bbesu\u02bbe o le malamalama ma le malosi masani o le ata, ae e leai se mea e mafai ona fa\u02bbamauina i le mua. E mafai ona fa\u02bbamaonia le malosi masani o le atunu\u02bbu atoa mai le amo, ma lenei lea e mafai ona mauaina se malosi fa\u02bbasa\u02bboina o le ata.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Metotia fa'atatau vave ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le folomia o nei ata ula e lua e mafai ona fa\u02bbamaonia ai se malosi masani e tusa ai ma le taimi na folomitia. O se seti o lua fuafuaga malamalama s1 ma s2 na fa\u02bbamauina i luga o se seti o ni faiga o le N i lauina o i latou o x, ua fa\u02bbailoa e x1, ... x1, ...:<math display=\"block\">s_j = \\sum_{k=1}^N{x_k^j}.<</ins>/<ins class=\"diffchange diffchange-inline\">math>A o le taumafai o nisi o nei folomitia, e mafai ona fa\u02bbaa\u02bboa\u02bbi ai ai nisi o lea e fa\u02bbamauina, o lea ua mafai ona fa\u02bbamaonia ai lea lagona o le malosi masani folomia i le taimi o lea</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">\\sigma = \\frac{\\sqrt{Ns_2 - s_1^2}}{N}<</ins>/<ins class=\"diffchange diffchange-inline\">math>I le taimi a luga, o le N, peitai ua tautumai i luga, o le saita o le seti o fiafia (po\u02bbo e mafai foi ona fa\u02bbasa\u02bbosa\u02bbo lea ma s0).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Feso'ota'i foi mo le malosi masani o le su\u02bbesu\u02bbega.<math display=\"block\">s = \\sqrt{\\frac{Ns_2 - s_1^2}{N(N - 1)}}.</math>I le faia o se galuega fa\u02bbapotopotoina, ina ua fa\u02bbasalalau auaunaga o nisi o nei sao sj, ua manaomia ona talitonu le galuega fa\u02bbasala, le puipuiga o le faitau, ma le faigata\u02bbaga o le faitau. O le metotia lalo na tusia e fa\u02bbamauina ai nisi o nei sao i le tulaga o le galuega fa\u02bbasala ma le taimi na teuteuina le latou faitau i le faitau. O lea ua mautinoa lea metotia e fa\u02bbamauina ai le su\u02bbesu\u02bbe o le n saofa\u02bbi i le tele o nisi o nisi sao fou, e leai ni taula na fautua i le taimi o le galuega. O le tulaga lenei e apiti ma le su\u02bbesu\u02bbe o le malosi masani e mafai ona tuuina atu i lea taimi ina ia fiafia ai.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mo k = 1,... , n :<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> A_0 &= 0\\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> A_k &= A_{k-1} + \\frac{x_k - A_{k-1}}{k}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>latalata i le A o le uiga.<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> Q_0 &= 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> Q_k &= Q_{k-1} + \\frac{k-1}{k} \\left(x_k - A_{k-1}\\right)^2 = Q_{k-1} + \\left(x_k - A_{k-1}\\right)\\left(x_k - A_k\\right)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>Manatua: Q 1 = 0 talu ai k \u2212 1 = 0 po\u02bbo x 1 = A 1 .</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Malosi Masani o le Su\u02bbesu\u02bbega</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">s^2_n = \\frac{Q_n}{n - 1}<</ins>/<ins class=\"diffchange diffchange-inline\">math>Malosi Masani o le Atunu\u02bbu Atoa:<math display=\"block\">\\sigma^2_n = \\frac{Q_n}{n}<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Fuafuaga mamafa ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I le fa\u02bbamauina o nisi o faiga o le xi i le galuega a le aafia ai o latou malosi wi, o le saita o lea o s0, s1, s2 e mafai ona fa\u02bbamauina uma:<math display=\"block\">s_j = \\sum_{k=1}^N w_k x_k^j</ins>.<ins class=\"diffchange diffchange-inline\">\\,</math>O le a leai ni faigofie i le vaega o le malosi masani</ins>. <ins class=\"diffchange diffchange-inline\">O s0 o le a leai ni numera o nisi, ae o le a le ni numera o malo\u02bbi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le metotia o le fa\u02bbamaoni i le malosi masani ma le faigaluega o le faia ai e mautinoa lea, ae o le a le ni auala o le a fa\u02bbaauau.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O se folomitia o le saita o malosi o latou tausaga o le a fa\u02bbamauina mo ia k mai le 1 i le n:<math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> W_0 &= 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> W_k &= W_{k-1} + w_k</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>ma luga o malo\u02bbi i le a fa\u02bbaaoga ai le 1</ins>/<ins class=\"diffchange diffchange-inline\">\u03c3 e fa\u02bbaopoopoina ai e wi</ins>/<ins class=\"diffchange diffchange-inline\">Wn</ins>:<ins class=\"diffchange diffchange-inline\"><math display=\"block\">\\begin{align}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> A_0 &= 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> A_k &= A_{k-1} + \\frac{w_k}{W_k}\\left(x_k - A_{k-1}\\right) \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> Q_0 &= 0 \\\\</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\"> Q_k &= Q_{k-1} + \\frac{w_k W_{k-1}}{W_k}\\left(x_k -A_{k-1}\\right)^2 = Q_{k-1} + w_k\\left(x_k-A_{k-1}\\right)\\left(x_k - A_k\\right)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\\end{align}</math>I le tu\u02bbuina muamua o le masini,<math display=\"block\">\\sigma^2_n = \\frac{Q_n}{W_n}\\,</math>ma<math display=\"block\">s^2_n = \\frac{Q_n}{W_n - 1},</math>pe<math display=\"block\">s^2_n = \\frac{n'}{n' - 1} \\sigma^2_n,</math>latalata i le n o nisi o mea uma, ma le n\u2032 o nisi o mea e leai ni malosi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O lea metotia luga e fa\u02bbamauina ai i luga e tatau ona mafai ai ona fai se metotia lagona o mea e tatau ona faia i le taimi o le galuega ma le malo, ma lea o lo\u02bbo mafai ai ona fai ai nisi o metotia ma lea e sili ona fa\u02bbamauina ai i luga.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Tala o le V\u0101 ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Na fa\u02bbatumuina le upu 'malosi masani' i le tusi e Karl Pearson i le 1894, i se taimi na ta\u02bbita\u02bbia ai lo latou faaauauina i le taimi o ia galuega. O lea ua faia i se fa\u02bbatonu mo nisi o su\u02bbesu\u02bbega ua na o latou itulau: ma lelei, na fa\u02bbaaoga e Gauss le upu 'mean error'.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Malosi Masani o le Itulau ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">O le Malosi Masani o le Itulau (SDI) e fa\u02bbaaoga i auala e fa\u02bbamaonia ai le malosi masani, ma fa\u02bbaaloalo atu i ai moa galuega o le fanau o le mataigatasi. E fa\u02bbamatalaina e lea pe aisea:<math display=\"block\">\\text{SDI} = \\frac{\\text{Laboratory mean} - \\text{Consensus group mean}}{\\text{Consensus group standard deviation}}<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Sualofoa A'oa'oga ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[File</ins>:<ins class=\"diffchange diffchange-inline\">MultivariateNormal.png|thumb| Le malosi masani o le a\u02bboa\u02bbo (lanu meamata) o se fausaga normal e lua-dimensions.]</ins>]</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">I itu e lua, e mafai ona fa'ata'ita'iina le va'aiga masani i le fa'asologa o le ellipse (silasila i le Multivariate normal distribution \u00a7 Geometric interpretation).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Vaai foi ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">\u00a0\u00a0</ins></div></td></tr>\n"
}
}