Àwọn

Ṣàfikún fálù àìdálẹ̀ láti inú ìpéwọ̀n z̀ láti wá ìpéwọ̀n rẹ̀.

Àwọn ìṣàmúlò-ètò —

Àwọn ààtòjú àwọn ààtòjú P(X ≤ x) —

P(X ≥ x) —

Àwọn Ààyè —

Àwọn Àtòjọ-ẹ̀yàn àwọn ìṣàmúlò-ètò

Ńlà àwọn àwọn ààtò àtòjọ-ẹ̀yàn yìí?

Àkóónú ìṣàmúlò-ètò yìí

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.

Àwọn Àtòjọ-ẹ̀yàn

Kini o tumọ si z-ìjádè tí 2?

A z-score of 2 means the value is two standard deviations above the mean. Under a normal distribution about 97.7% of values fall below it, so it is a fairly extreme, high value.

Àwọn ìṣàmúlò-ètò àwọn ìṣàmúlò-ètò

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.

Bawo ni mo ṣe lè ṣé ìṣàmúlò-ètò z-score?

Ṣàfikún aago lọ́wọ́lọ́wọ́ láti inú àwọn fálù rẹ̀ àti pàrá nípa ìṣàfarawé: z = (x − μ) / σ. Fun x = 85, μ = 70 àti σ = 10 z-ìpílẹ̀ jẹ́ (85 − 70) ÷ 10 = 1.5.

Bawo ní àwọn ìtàn-z̀ tí wọ́n bá jẹ́ ìṣàfarawé àwọn ìtàn-ọ̀kan?

The z-score is converted to a percentile through the standard-normal cumulative distribution, which gives the proportion of values below it. A z-score of 0 is the 50th percentile, +1 is about the 84th and −1 about the 16th.

Àwọn àwọn ààyè-iṣẹ́ wò nínú àwọn ààyè-iṣẹ́ àwọn ààyè-iṣẹ́

Ninu ofin ti o wọpọ, awọn z-iwọn ti o ju ±2 lọ jẹ ti ko wọpọ ati pe o kere ju ±3 lọ, nitori pe nipa 95% ti ibaraẹnisọrọ ti o wọpọ wa laarin awọn iyatọ meji ti o wọpọ ati 99.7% laarin mẹta.

Ń fẹ́ ìṣàfarawé àwọn ààyè-iṣẹ́ ìṣàfarawé àwọn ààyè-iṣẹ́?

O lè fi àwọn fálù wò nínú ìpèwọ̀n fún àwọn fálù z nípa ìṣàfarawé àwọn ìṣàmúlò-ètò, àwọn ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò àwọn ìṣàmúlò-ètò yìí nínú àwọn àtòjọ-ẹ̀yàn àwọn àtòjọ-ẹ̀yàn. Fún àwọn àtòjọ-ẹ̀yàn tí a kò fi àwọn ìṣàmúlò-ètò yìí ṣe nínú àwọn ìṣàmúlò-ètò náà.

API — ló àwọn ìṣàmúlò-ètò yìí láti inú ìṣàmúlò-ètò

Fi àwọn ìṣàmúlò-ètò yìí kọ̀ǹpútà yìí láti jẹ́ ààyè-iṣẹ́ JSON tí a tí fi pamọ́ - kò ní bọ́tìnì kan tí a fẹ́. Fi àwọn fálù ààyè-iṣẹ́ sílẹ̀ sí bí àwọn àwọn ìṣàmúlò-ètò àti JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Ka àwọn àkọlé API kíkún →

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

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);

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

Àkóónú ìṣàmúlò-ètò yìí

Àwọn Àtòjọ-ẹ̀yàn

Àwọn Ìṣàmúlò-ètò Ìṣàmúlò-ètò

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

curl

JavaScript fetch()

JavaScript `fetch()`