Standard Deviation Calculator

Calculate sample or population standard deviation, variance and mean.

Standard deviation —

Variance —

Mean —

Sum of squared deviations —

Chimwe chinhu —

Maximum —

Range —

Kuverenga —

Zvinyorwa zvinogadziridzwa paunenge uchinyora.

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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.

Zvimwe zvinobvunzwa zvakanyanya

Chii chinonzi chiyero chekuenzanisa pakati pezviuru zvevanhu nezviuru zvevanhu?

The population formula inoparadza summed squared deviations ne n; sample formula inoparadza ne n - 1. The n - 1 (Bessel’s kugadziriswa) inobhadharisa yechokwadi kuti sample anofarira kufungidzira pasi chikuru kupararira kwevanhu yaiva kubva.

Nei square deviation?

Squarering inoita kuti chero deviation iite zvakanaka kuti varege kubvisa, uye inowedzera kuoma kwezvikuru zvikanganiso. Kutora rudzi rwesquare pakupera kunodzosera chiyero kune zvakasikwa zvedata.

Ndinogona sei ku calculate standard deviation by hand?

Find the mean, subtract it from each value to get the deviations, square each deviation and add them up, then divide by n − 1 for a sample or n for a population and take the square root of that result.

Chii chinonzi standard deviation?

Hapana "yakanaka" kukosha kwese kwese — inoenderana nehuwandu hwedata rako uye nemamiriro ayo. Standard deviation inoreva chete kuti iri pedyo nepakati; iyo imwe shanduko idiki yemitengo yezvivakwa inogona kuve yakakura kwazvo kune zvibodzwa zvebvunzo. Coefficient of variation inotaura nezve iyo sechikamu chemazana chepakati chekuenzanisa.

Chiyero chekuchinja chinogona kunge chiri zero kana chiri kuipa?

Izvi zvinogona kunge zvakaipa, nekuti zvinowanzova nesimba rekuti zviite kuti zvive zvakaipa, nekuti zvinowanzova nesimba rekuti zviite kuti zvive zvakaipa, nekuti zvinozoita kuti zvive zvakaipa.

Nei mufananidzo ku kalkuleta inofanira kuiswa pamwechete zviviri zvibereko?

The sample formula inoparadzaniswa ne n - 1, saka imwe chete pfungwa ichaparadzana ne zero uye inodzokera kusingazivikanwe. A sample standard deviation chete anoreva kana iwe uine maviri kana akawanda zviyeuchidzo kuti uenzanise.

API — kushandisa iyi kalkulator kubva code

Nhare iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo mavara pasi separameter query kana JSON. Chii zvachose chaunoisa kunze chinoshandisa default iyo peji iri rakasviba nayo; parameter isiri yechokwadi inonzi 400, uye haisi zero. Tora yakazara API docs →

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);

Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.

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Zvimwe zvinobvunzwa zvakanyanya

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Endpoint

curl

JavaScript fetch()

JavaScript `fetch()`