Confidence Interval Calculator
Kugadzira confidence interval yepakati kubva ku sampling mean, SD uye size.
Zvinyorwa zvinogadziridzwa paunenge uchinyora.
Nezve iyi kalkulator
A confidence interval gives a range that is likely to contain the true population mean, estimated from a sample. Instead of a single best guess it reports a band together with a confidence level that says how often such bands capture the true value.
This calculator uses the z-interval: mean ± z*·(σ / √n), where z* is the standard-normal critical value for your chosen confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%) and σ / √n is the standard error. It reports the bounds, the margin of error and the standard error, and a table shows the interval at the 90%, 95% and 99% levels so you can see how the range widens as you demand more confidence.
Worked example: a sample mean of 100 with a standard deviation of 15 and 50 observations has a standard error of 15 ÷ √50 ≈ 2.12. At 95% confidence the margin is 1.96 × 2.12 ≈ 4.16, giving an interval of about 95.84 to 104.16. The z-interval suits large samples (roughly n ≥ 30) or a known population standard deviation; for small samples use a t-interval instead.
Zvimwe zvinobvunzwa zvakanyanya
Chii chinonzi 95% confidence interval?
Izvi zvinoreva kuti kana iwe wakawedzera kuongorora nguva zhinji uye wakagadzira nguva yepakati nguva nenguva, pamusoro pe95% yenguva dzepakati dzichave nechokwadi chevanhu. Izvi hazvireve kuti pane 95% mukana wekuti nguva yepakati iri mune imwe nguva yepakati.
Kana ndichifanira kushandisa t-interval sezvandinoda?
Usashandisa t- interval kana mufananidzo uri muto (pasi pe30) uye standard deviation yevanhu haizivikanwe. The t- distribution has heavier tails, giving a slightly wider, more cautious interval than this z- based one.
Chii chinonzi margin of error munguva yekuvimbika?
The margin of error is the half-width of the interval, z*·(σ / √n). You add and subtract it from the sample mean to get the upper and lower bounds, so a smaller margin means a more precise estimate.
Ndinogona sei kuita kuti confidence interval iite seyakavhara?
Kuunganidza a zhinji muenzaniso, sezvo width zvishoma ne square root of n, kana kubvuma pasi confidence level. Kuderedza variability mu data yakowo tightens the interval. Quadrupling muenzaniso urefu approximately halfs the width.
Iine a yepamusoro confidence level kuita interval yakakura?
Ndinoda. Kuda zvakawanda kuvimbika inoshandisa zhinji zvikuru kukosha z *, saka 99% interval ikuru kupfuura 95% interval yakavakwa kubva pamwechete data. Zvinoramba paine trade-off pakati kuvimbika uye kunyatsoita.
Chii chinonzi standard error?
Standard error i standard deviation yakaparadzana ne square root ye sample size (σ / √n). Inoita kuti uzive kuti sample mean yacho ichasiyana sei kubva ku sample kuenda ku sample, uye ndiyo inoita kuti uzive kuti ndeipi nzira yekuzvidzivirira kubva kune izvi.
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/confidence-interval/curl
curl "https://calculator.free/api/v1/confidence-interval/?mean=100&sd=15&n=50&conf=1.96"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/confidence-interval/?" + new URLSearchParams({
"mean": "100",
"sd": "15",
"n": "50",
"conf": "1.96"
}));
const data = await r.json();
console.log(data.results);Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.