I-Calculator ye-Z-Score

Guqula inani elimnyama libe yiz-score z bese uthola i-percentile yayo.

Isilinganiso se-Z —

Izinga le-percentile P(X ≤ x) —

P(X ≥ x) —

Indawo —

Iziphetho zivuselelwa uma ubhala.

Ingabe le calculator ikulethela impendulo efanele?

Malunga nale khadi

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.

Imibuzo ebuzwa kaningi

Yini okusho i-z-score ye-2?

Izinga le-z le-2 lisho ukuthi ixabiso liyizinhlamvu ezimbili ezijwayelekile eziphezulu kwezinga. Ngesihlukaniso esijwayelekile, cishe i-97.7% yamaxabiso awela ngaphansi kwayo, ngakho-ke iyinani eliphakeme, eliphakeme.

Ingabe i-z-score ingabi yikho?

Yebo. Izinga le-z eli Negative lisho ukuthi inani lingaphansi kwezinga eliphakathi. Izinga le-z le -1.5, isibonelo, liyi-standard deviations eyodwa nengxenye ngaphansi kwezinga eliphakathi.

Ngiyibala kanjani i-z-score?

Khubaza umphakathi kusuka kuxabiso lakho bese uhlukanisa ngezinga elijwayelekile lokuhluka: z = (x − μ) / σ. X = 85, μ = 70 ne σ = 10 i-z-score yi (85 − 70) ÷ 10 = 1.5.

Uyini umphumela we-z ophathelene nephesentiyeli?

I-z-score iguqulwa ibe yi-percentile nge-standard-normal cumulative distribution, enikeza inhlanganisela yamaxabiso angaphansi kwayo. I-z-score ka-0 iyi-percentile ye-50th, +1 iyi-84th kanye ne-−1 i-16th.

Yini ethathwa njenge z-score ephakeme noma engajwayelekile?

Ngomthetho ojwayelekile we-thumb, ama-z-scores angaphezu kwe-±2 ajwayelekile futhi angaphezu kwe-±3 avame ukutholakala, njengoba cishe i-95% yokwabelana okujwayelekile itholakala ngaphakathi kwezinguquko ezimbili ezijwayelekile zesilinganiso kanye ne-99.7% ngaphakathi kwezithathu.

Ingabe ngidinga ukuhlukaniswa okujwayelekile ukusebenzisa i-z-score?

Ungabeka noma yiluphi uphawu ngefomula ye-z ngaphandle kokubheka ifomu, kodwa i-percentile ne-tail probabilities le thuluzi likhombisa ukuthi idatha ilandela ukusabalalisa okujwayelekile. Ku-data eqinile engajwayelekile, lezi zici ziyi-approximate.

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/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);

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

Malunga nale khadi

Imibuzo ebuzwa kaningi

Ama-calculators ahlobene

Ingxenye yendawo

curl

JavaScript fetch()

JavaScript `fetch()`