Kaitirotiro pānui
Ka tatau i te tauira, te iwi whānui rānei i te whakarerekētanga paerewa, te rerekētanga me te tauwaenga.
Ka whakahōutia ngā hua i te wā e tātuhi ana.
Mo tēnei tātaitai
Standard deviation measures how spread out a data set is around its mean: a small value means the numbers cluster tightly near the average, a large one means they are widely scattered. This calculator computes both the sample standard deviation (dividing the sum of squared deviations by n − 1, Bessel’s correction) and the population standard deviation (dividing by n), and reports the variance, mean, range and the sum of squared deviations it used. Choose sample when your numbers are a subset drawn from a larger group, and population when they are the entire group.
The method has four steps: find the mean, subtract it from each value to get the deviations, square those deviations and add them up, then divide by n − 1 (sample) or n (population) and take the square root. The square root returns the answer to the same units as the original data, which is why standard deviation is usually preferred over variance for interpretation.
Worked example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The squared deviations sum to 32, so the population variance is 32 ÷ 8 = 4 and the population standard deviation is √4 = 2; the sample version divides 32 by 7, giving about 4.57 and a standard deviation of roughly 2.14. The deviation table below shows each value’s distance from the mean and its squared deviation so you can follow the calculation.
Ko nga pātai e pā ana
He aha te rerekētanga i waenganui i te tauira me te whakarerekētanga paerewa o te iwi whānui?
Ka wehe te tātai iwi whānui i ngā rerekētanga tapawhā tāpiri e n; ka wehe te tātai tauira e n − 1. Ko te n − 1 (whakarereketanga a Bessel) e whakamutu ana i te mea ka whakaiti te tauira i te tuaritanga pono o te iwi whānui i puta mai ai.
He aha te tapawhā o ngā whakarerekētanga?
Ka whakawātea te tapawhā i ia nekehanga tōrunga kia kore ai rātau e whakakore, ā, ka nui ake te taumaha o ngā nekehanga nui ake. Mā te tango i te pūtake tapawhā i te mutunga ka hoki te inenga ki ngā wae o te taketake o te raraunga.
He pēhea te tatau i te rerekētanga paerewa mā te ringa?
Ka kitea te tauwaenga, ka tangohia i ia uara hei whiwhi i ngā rerekētanga, te tapawhā o ia rerekētanga me te tāpiri i a rātou, kātahi ka wehea e n − 1 mō tētahi tauira, n rānei mō te iwi whānui, ā, ka tangohia te pūtake tapawhā o taua hua.
He aha te rerekētanga paerewa pai?
Kāore he uara "whakapaia" katoa - e whakawhirinaki ana ki te tauine me te horopaki o tōtou raraunga. He mea nui noa iho te rerekētanga paerewa e tata ana ki te waenganui; ko te whakawhānuitanga ōrite he iti noa iho mō ngā utu whare ka tino nui mō ngā pūkete whakamātautau. Ko te tauwhāiti o te rerekētanga e whakapuakina ana hei ōrautanga o te waenganui mō te whakataurite.
He kore te whakarerekētanga paerewa, tōraro rānei?
Ka kore pea, e puta ana anake ina ōrite ia uara, ā, kāore he horahanga i te katoa, kāore pea i te āhua tōraro, nā te mea ko te pūtake tapawhā o te tau tōpū o ngā tau tapawhā.
He aha te hiahiatia e te tātaitanga tauira kia rua ngā uara i te iti rawa?
Ka wehea te tātai tauira e n − 1, kia taea ai e tētahi uara kotahi te wehe i te kore, ā, ka waiho i te kore tautuhi. He tikanga anake te whakarerekētanga paerewa tauira ina rua, neke atu rānei o ngā kitenga kia whakatauritetia.
API — whakamahi tēnei tātaitai mai i te waehere
E kī ana tēnei tātaitai hei wāhi mutunga kore JSON - kāore he kī e hiahiatia ana. Ka tukuna ngā uara āpure i raro nei hei tohutoro pātai, JSON rānei. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Ka pānui te papatono API katoa →
Whakamutunga
GET https://calculator.free/api/v1/standard-deviation/curl
curl "https://calculator.free/api/v1/standard-deviation/?numbers=9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4&type=sample"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/standard-deviation/?" + new URLSearchParams({
"numbers": "9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4",
"type": "sample"
}));
const data = await r.json();
console.log(data.results);Ko ngā hua he whakataunga mō te tohutohu ahuwhānui anake, ehara i te tohutohu moni, rongoā, tāke rānei.