Kalkulatè deviation estanda
Kalkile deviation estanda, varyasyon ak mwayèn nan yon echantiyon oswa popilasyon.
Rezilta yo mete ajou pandan w ap ekri.
Atik sa a
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.
Kesyon ki poze souvan
Ki diferans ki genyen ant deviation estanda echantiyon ak deviation estanda popilasyon?
Formule popilasyon an divize deviations kare totalize pa n; fòmile echantiyon an divize pa n - 1. n - 1 (koryasyon Bessel) konpanse pou lefèt ke yon echantiyon gen tandans pou sous-estime la distribisyon reyèl nan popilasyon an li te soti nan.
Poukisa kare deviations?
Squarering fè chak deviation pozitif konsa yo pa anpeche deyò, epi li pwa pi gwo deviations pi lou. Te pran ranje kare nan fen a retounen mezi a nan orijinal unite nan done yo.
Ki jan pou mwen kalkule deviation estanda pa men?
Jwenn mwayèn la, retire li soti nan chak valè pou jwenn deviations yo, kare chak deviation ak ajoute yo, Lè sa a, divize pa n − 1 pou yon echantiyon oswa n pou yon popilasyon ak pran ranje kare a nan rezilta a.
Ki sa ki se yon bon deviation estanda?
Pa gen okenn valè "bon" universal - li depann tout antye sou gwosè ak kontexte nan done ou. Yon deviation estanda se sèlman yon sans nan bò kote mwayèn; menm pwopagasyon ki se ti pou pri kay ka etonan pou pwen egzamen. Kowòdone varyasyon an eksprime li kòm yon pousan nan mwayèn pou konparezon.
Èske deviation estanda ka zero oswa negatif?
Li ka zewo, ki rive sèlman lè chak valè se menm jan ak pa gen okenn dega nan tout. Li pa janm negatif, paske li se ranje kare a nan yon mwayèn de nimewo kare.
Poukisa calcul echantiyon an bezwen omwen de valè?
Formule a divize pa n - 1, se konsa yon valè sèl ta divize pa zewo epi li pa defini. Yon deviation estanda echantiyon sèlman gen sans lè ou gen de oswa plis observations pou konpare.
API — itilize sa a calculateur soti nan kòd
Apèl sa a calculateur kòm yon gratis JSON pwent-de-fini - pa gen okenn kle ki nesesè. Envoye valè jaden anba a kòm paramèt kesyonè oswa JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Li dokiman API a an antye →
Endpoint
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);Rezilta yo se estimasyon pou kòmandman jeneral sèlman, pa finansye, medikal oswa konsèy taks.