Ixabiso le Standard Deviation

Bala umzekelo okanye uluhlu loqoqosho olusezantsi lokutshintsha, uguquko kunye nexesha eliphakathi.

Ithambeka Elisezantsi —

Utshintsho —

Ixabiso eliphakathi —

I-sum ye-squared deviations —

Ubungakanani obuncinci —

Ubukhulu —

Igama le projekti —

Ibala —

Iinketho ze projekti

Ingaba le calculator ikunika umyalezo olungileyo?

Malunga nale Calculator

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 ebuza rhoqo

Yintoni utshintsho phakathi kwesampuli kunye nokungalingani okuqhelekileyo koqoqosho?

Ifomula yobalo-manani ihlula i-summed squared deviations nge-n; ifomula yovavanyo ihlula nge-n − 1. I-n − 1 (ukulungisa kwe-Bessel) ihlawulisa isizathu sokuba uvavanyo luya kuqikelela ngaphantsi ukusasazeka kwenyaniso kobalo-manani oluvela kulo.

Kutheni ubeka i-square kwi-deviations?

Ukwenza i-square iyenza yonke i-deviation i positive ukuze ingarhoxisi ngaphandle, kwaye iphakamisa i-deviations enkulu ngakumbi. Ukuthabatha i-square root kwisiphelo ibuyisela uvavanyo kwiyunithi yokuqala ye data.

Ndibala njani utshintsho olusezantsi oluqhelekileyo ngesandla?

Fumana umbindi, shiya ixabiso ngalinye ukuze ufumane utshintsho, ujikeleziso ngalunye lotshintsho kwaye udibanisa, emva koko udibanise nge n - 1 kumzekelo okanye n kuqoqosho kwaye uthathe umngcambu wesikwere womsebenzi.

Yintoni i-standard deviation elungileyo?

Akukho xabiso elipheleleyo "elilungileyo" - lixhomekeke ngokupheleleyo kubungakanani kunye nemeko ye data yakho. Ukusuka ngokuqhelekileyo kubhekisa kuphela kufutshane nomda; unikezelo olufanayo oluncinci kwixabiso lendlu lunokuba lukhulu kwinqaku lovavanyo. Ixabiso elilinganayo lotshintsho libonisa njengeepesenti yomda wothelekiso.

Ingaba ukuguquka okuqhelekileyo ku zero okanye ku negalelo?

Inoku kwenziwa ibe yi zero, eyenza ukuba ixabiso lifana kwaye akukho kusasazeka. Ayikwazi ukuba yi negative, kuba yi square root ye average of squared numbers.

Kutheni ubalo lwesampulu lufuna amaxabiso amabini?

Umzekelo wefomula uhlula nge n - 1, ngoko ixabiso elinye liya hlula nge zero kwaye lishiye olungachazwanga. Umzekelo wendlela yokungalingani ithetha kuphela xa uneemboniselo ezimbini okanye ngaphezulu zokuthelekiswa.

API — sebenzisa le calculator ukusuka kwikhowudi

Nceda le khadi lemali njengendawo esemva ye-JSON ekhululekileyo - akukho qhosha lifunekayo. Thumela amaxabiso endawo ezantsi njengeparameter yombuzo okanye i-JSON. Nantoni na oyenzayo isebenzisa okungagqibekanga okufanayo eli phepha ligqityiwe ngaphambili; iparameter engaziwayo yi 400, ayikho i zero ekhululekileyo. Funda i-API epheleleyo →

Incopho yesiphelo

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);

Results are estimates for general guidance only, not financial, medical or tax advice.

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Incopho yesiphelo

curl

JavaScript fetch()

JavaScript `fetch()`