I-Calculator ye-Standard Deviation

Balala isibonisi noma inani lesimo esijwayelekile sokungalingani, ukuhluka kanye nesilinganiso.

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Iziphetho zivuselelwa uma ubhala.

Ingabe le calculator ikulethela impendulo efanele?

Malunga nale khadi

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.

Imibuzo ebuzwa kaningi

Yini ushintsho phakathi kwesampula nesilinganiso sokungalingani komphakathi?

Ifomu le-population lihlukanisa i-summed squared deviations ngo-n; ifomu lesampula lihlukanisa ngo-n - 1. I-n - 1 (ukulungisa kuka-Bessel) ikhokhela iqiniso lokuthi isampula ivame ukulinganisela ngaphantsi ukusakazeka kweqiniso kwe-population eyavela kuyo.

Kungani ubeka i-square ku-deviations?

Ukuhlukaniswa kwenza wonke amaphutha abe ngcono ukuze angalahleki, futhi abeke isisindo kumaphutha amakhulu kakhulu. Ukuthathela umsuka wesikwere ekugcineni kubuyisela umlinganiselo kumayunithi angaphambili wedatha.

Ngiyibala kanjani i-standard deviation ngesandla?

Thola umphakathi, shiya ixabiso ngalinye ukuze uthole izilinganiso, hlanganisa zonke izilinganiso bese ungeza, bese uhlukanisa ngo n - 1 ngesampula noma n ngezinga lomphakathi bese uthatha isitshalo se-square root semiphumela.

Yini i-standard deviation engcono?

Akukho lutho oluphelele "oluhle" ixabiso - lixhomekeke ngokuphelele ku isilinganiso kanye nesimo sedatha yakho. Iphutha elijwayelekile liyiqiniso kuphela eduze kwephakathi; i-spread efanayo encane kakhulu kuntengo yendlu ingaba enkulu kakhulu kumazinga wokuhlolwa. I-coefficient yehlukana ichaza njengephesenti lephakathi kokulinganisa.

Ingabe isilinganiso sokungalingani siyi zero noma si negative?

Ingaba yi-zero, okuzokwenzeka kuphela uma ixabiso ngalinye lifana futhi akukho ukusakazeka ngaso sonke isikhathi. Ngakho-ke, ngeke kube yi-negative, ngoba yi-square root yesilinganiso se-squared numbers.

Kungani isampula yokulinganisa idinga amaxabiso amabili?

Ifomu lesibonelo lihlukaniswa nge n - 1, ngakho inani elilodwa lihlukaniswe nge zero futhi lishiye lingazibonakalisi. Isibonelo sesimo se-standard deviation sizothola lutho uma unezifundo ezimbili noma ngaphezulu zokuqhathanisa.

API — sebenzisa le calculator kusuka kukhodi

Nquma le calculator njenge JSON evulekile yendawo yokuqeda - akukho isithonjana esidingekayo. Thumela amaxabiso endawo ngezansi njengezilungiselelo zombuzo noma i-JSON. Noma yini ongayishiya isebenzisa iphutha elifanayo elifakwe ngaphambili lekhasi; ipharamitha engaziwa yi-400, ayikho i-zero emnyama. Funda i-API egcwele →

Ingxenye yendawo

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);

Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.

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Ingxenye yendawo

curl

JavaScript fetch()

JavaScript `fetch()`