Mhesabu Mkosa - Kosa

Pata nafasi ya kupita kiasi katika uchunguzi.

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Asilimia ya watu wanaojibu kwa njia fulani, asilimia 50 ndio wenye kushikilia sana maoni yao.
Mzozo wa makosa —
Kufungwa Chini —
Sehemu ya juu ikifungwa —
Upana —

Matokeo yanakuwa bora zaidi unapochapa.

Je, hesabu hiyo ilikupa jibu linalofaa?

Kuhusu kifaa hiki cha kupigia hesabu

The margin of error tells you how far a survey result is likely to be from the true population value — the "plus or minus" figure quoted next to poll results. For a proportion it is z*·√(p(1 − p) / n), where p is the sample proportion, n the sample size and z* the critical value for your confidence level (1.96 for 95%).

It reports the margin, the confidence-interval bounds around your proportion and the full interval width, and a table shows how the margin shrinks as the sample grows. The default 50% proportion gives the most conservative (largest) margin, because the quantity p(1 − p) peaks at p = 0.5, which is why pollsters often quote it.

Worked example: with 1,000 respondents split 50/50 at 95% confidence, the margin is 1.96 × √(0.5 × 0.5 ÷ 1000) ≈ 1.96 × 0.0158 ≈ 3.1 percentage points. So a poll result of 50% really means somewhere between about 46.9% and 53.1%. To halve that margin you would need roughly four times the sample.

Maswali yaliyoulizwa mara nyingi

Kwa nini sampuli kubwa zaidi hupunguza kosa?

Sehemu ya katikati ya mchanga hupunguka na kuwa ndogo sana, kwa hiyo ikizidi kufikia nusu ya ncha ya kosa.

Kwa nini asilimia 50 ndio kiwango kisicholingana?

The quantity p(1 − p) is largest at p = 0.5, so assuming a 50/50 split produces the widest, most conservative margin of error. Using it guarantees the true margin is no larger than reported.

How do I calculate the margin of error?

Multiply the critical value z* for your confidence level by the square root of p(1 − p) ÷ n. For p = 0.5, n = 1000 and 95% confidence, that is 1.96 × √(0.25 ÷ 1000) ≈ 3.1 percentage points.

Kuna tofauti gani kati ya kosa na kipindi cha katikati cha uhakika?

Sehemu ya katikati ya makosa ni nusu -wid; kipindi cha uhakika ni kiwango unachopata kwa kuongeza na kuondoa nafasi ya matokeo. Asilimia 48 ya matokeo kwa pambizoni 3 hutoa kipindi cha uhakika cha asilimia 45 hadi 51.

Je, idadi kubwa zaidi ya watu huhitaji kuwe na kadiri kubwa zaidi ya kosa?

Zaidi ya maelfu machache ya watu wanatoshana na watu wachache tu kwenye nafasi ya kati ya mambo yaliyo ya ukubwa wa sampuli. Ndiyo sababu kura ya kitaifa na kura ya maoni ya jijini inaweza kuwa na nafasi ileile kwa idadi ileile ya waliohojiwa.

Kiwango cha uhakika hubadilije ubaya?

A higher confidence level uses a larger z*, which widens the margin. Moving from 95% (z* = 1.96) to 99% (z* = 2.576) increases the margin by about 31% for the same sample.

Vifaa vya Kupima Gharama

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API bustanini hutumia kifaa hiki cha hesabu kutoka kwenye mfumo wa sheria

Ipigie simu kifaa hiki cha kupigia hesabu kama Junse É not doot toder. Chochote unachoacha kinatumia kiwango kilekile cha mwisho ambacho ukurasa huu haujakamilika; parameta isiyojulikana ni 400, si sufuri kimya kamwe. Soma habari kamili za API docs →

keyboard label

GET https://calculator.free/api/v1/margin-of-error/

curl

curl "https://calculator.free/api/v1/margin-of-error/?n=1000&p=50&conf=1.96"

JavaScript fetch()

const r = await fetch(
  "https://calculator.free/api/v1/margin-of-error/?" + new URLSearchParams({
    "n": "1000",
    "p": "50",
    "conf": "1.96"
  }));
const data = await r.json();
console.log(data.results);

Matokeo ni makadirio ya mwongozo wa ujumla, si wa kifedha, wa kitiba au wa kodi tu.