Z-Score Calculator

Kushandura a raw kunaka kuti a z- score uye tsvaga yake percentile.

Z-score —

Percentile P(X ≤ x) —

P(X ≥ x) —

Position —

Zvinyorwa zvinogadziridzwa paunenge uchinyora.

Did this calculator give you the right answer?

Nezve iyi kalkulator

A z-score (standard score) tells you how many standard deviations a value lies above or below the mean: z = (x − μ) / σ. A positive z-score sits above the mean, a negative one below, and a z-score of zero is exactly at the mean. Standardising this way lets you compare values measured on completely different scales.

This calculator also returns the percentile — the probability that a value from a normal distribution is below x — and the right-tail probability, using the standard-normal cumulative distribution computed with an accurate error-function approximation, and it plots where x sits on the bell curve.

Worked example: if a test has a mean of 70 and a standard deviation of 10, a score of 85 gives z = (85 − 70) ÷ 10 = 1.5, meaning it is one and a half standard deviations above average. Under a normal distribution about 93.3% of scores fall below it, so it lands at roughly the 93rd percentile. Z-scores are the basis of standardised testing, quality control and the "68–95–99.7" rule.

Zvimwe zvinobvunzwa zvakanyanya

Chii chinonzi z-score ye2?

A z-score ye 2 zvinoreva kuti mitengo iri maviri standard deviations pamusoro pepakati. Pashure a normal distribution pamusoro 97.7% mitengo kusvikira pasi, saka iri zvakakwana zvakaoma, yepamusoro mitengo.

Z-score inogona kunge iri yakaipa?

Yes. A negative z-score simply means the value is below the mean. A z-score of −1.5, for example, is one and a half standard deviations below the average.

Ndiani anofanira kuisa mari yemubhadharo?

Kubvisa pakati kubva panzvimbo yako uye kuparadzana ne standard deviation: z = (x − μ) / σ. Kuti x = 85, μ = 70 uye σ = 10 z-score ndeye (85 − 70) ÷ 10 = 1.5.

Maitiro ekubatanidza z-score kune percentile?

Z-score inoshandurwa kuita percentile kuburikidza nestandard-normal cumulative distribution, iyo inotipa chikamu chemavara pasi pake. A z-score ye0 ndeye 50th percentile, +1 ndeye 84th uye -1 ndeye 16th.

Chii chinoonekwa sechikuru kana chisina kujairika z-score?

Nechirevo chinozivikanwa, z-scores pamusoro pe±2 hazvina kujairika uye pamusoro pe±3 zvinonetsa, sezvo pamusoro pe95% yeiyo normal distribution iri mukati mezviviri standard deviations yepakati uye 99.7% mukati me3.

Ndinofanira here kushandisa normal distribution kuti ndiwane z-score?

Unogona kunyatsoita kuti chero chinhu chiite sezvakanyorwa nez formula, pasina kunyatsofunga nezvemufananidzo, asi percentile netail probabilities iyi tool reports inofunga kuti data rinotevera kugoverwa kwezvinyorwa.

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/z-score/

curl

curl "https://calculator.free/api/v1/z-score/?x=85&mean=70&sd=10"

JavaScript `fetch()`

const r = await fetch(
  "https://calculator.free/api/v1/z-score/?" + new URLSearchParams({
    "x": "85",
    "mean": "70",
    "sd": "10"
  }));
const data = await r.json();
console.log(data.results);

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

Nezve iyi kalkulator

Zvimwe zvinobvunzwa zvakanyanya

Maitiro ekuita Calculators

Endpoint

curl

JavaScript fetch()

JavaScript `fetch()`