I-Calculator ye-Variance
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Variance is the average of the squared deviations from the mean and is the square of the standard deviation. This calculator gives the sample variance (sum of squared deviations divided by n − 1) or the population variance (divided by n), along with the standard deviation, mean, range and sum of squared deviations. Variance is expressed in squared units, which is why the standard deviation — its square root — is usually easier to interpret.
To find it, take the mean, subtract it from every value, square each of those deviations, add them together and divide by n − 1 for a sample or by n for a whole population. Squaring is what makes variance always non-negative and gives extra weight to values that lie far from the mean.
Worked example: for 12, 15, 17, 20, 22, 25 the mean is 18.5. The squared deviations sum to about 118.5, so the sample variance is 118.5 ÷ 5 = 23.7 and the population variance is 118.5 ÷ 6 = 19.75. Variance is the workhorse behind ANOVA, portfolio risk, quality control and many other techniques; the deviation table below lists each value’s distance from the mean and its square.
Imibuzo ebuza rhoqo
Utshintsho luqhagamshelana njani nokungalingani okuqhelekileyo?
Ixabiso eliqhelekileyo liyintloko yesikwere sexabiso eliguqukayo. Ixabiso eliguqukayo likwiyunithi eziskwayeriweyo (umzekelo, iidola eziskwayeriweyo), ngelixa ixabiso eliqhelekileyo libuyela kwiyunithi zokuqala, ngoko ke zombini zisoloko zichaza unikezelo olufanayo.
Ndisebenzisa njani i n versus n − 1?
Yahlula nge n - 1 xa i data yakho ibonisa umzekelo osetyenziswayo ukuqikelela uqoqosho olukhulu; yahlula nge n xa i data yakho ibonisa uqoqosho olupheleleyo olumkelayo.
Kutheni i-variance ikwiyunithi ezi-2?
Kuba utshintsho ngalunye lubekwa kwisikwere phambi kokulinganisa, impumelelo ithatha isikwere seyunithi yokuqala - iidola ezikwisikwere, isentimitha ezikwisikwere njalo njalo. Oku kwenza utshintsho lunzima ukuchaza ngokuthe ngqo, oko kubangela ukuba isiseko sayo esikwisikwere, utshintsho oluqhelekileyo, lunikezelwe ngaphaya kwayo.
Ingaba utshintsho luya kuba lu negative?
Ayinaku. Yiphakathi yamanani aphindwe kabini, ngoko ke iyaqhubeka ibe yi zero okanye i positive. Utshintsho lwe zero ngokuchanekileyo kuthetha ukuba ixabiso ngalinye kumqolo lufana.
Yintoni utshintsho phakathi kwe-variance ne-standard deviation?
Zichaza unikezelo olufanayo kodwa kwiimlinganiselo ezahlukeneyo: uguquko luphakathi kokungalingani okuthe nkqo, nokungalingani okuthe nkqo kukungcambu okungenani, emva kwiyunithi yokuqala. Ukuba uguquko luyi-25, ukungabinani okuthe nkqo ku-5.
Isetyenziswa njani i-variance kuhlalutyo olunyanzelekileyo?
Utshintsho luyisiseko somngcipheko kwimali, amandla ophawu kwizobugcisa kunye novavanyo lwe-F kwi-ANOVA, apho utshintsho phakathi kwamaqela luthelekiswa notshintsho ngaphakathi kwabo ukugqiba ukuba ngaba amaqela athetha ukuba hlukile.
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/variance/curl
curl "https://calculator.free/api/v1/variance/?numbers=12, 15, 17, 20, 22, 25&type=sample"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/variance/?" + new URLSearchParams({
"numbers": "12, 15, 17, 20, 22, 25",
"type": "sample"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.