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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.
Imibuzo ebuza rhoqo
Kutheni isampula enkulu ikhupha umda wemposiso?
Umda ukhuphuka ngesiseko esikwere sobungakanani besampuli, ngoko ukuphindaphinda i n iphindwe kabini umda wemposiso. Olu buyiselo olunciphayo luthetha ukuba isampuli enkulu kakhulu ifuneka ukutsala umda ngaphantsi kwesinye okanye iindawo ezimbini zepesenti.
Kutheni i-50% isetyenziswa njengenani elimiselweyo?
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.
Ndibala njani umda wemposiso?
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.
Yintoni utshintsho phakathi kwe-margin yemposiso kunye nexesha lokuphumla lokunyaniseka?
Umda wemposiso ngububanzi obuphezu kwesinye; umda wokungaqiniseki kuluhlu olupheleleyo olufumanekayo ngokudibanisa nokukhupha umda kwiziphumo zakho. I-48% yeziphumo nomda we-3-incopho unika umda wokungaqiniseki we-45% ukuya kwi-51%.
Ingaba uqoqosho olukhulu lufuna umda omkhulu wokungalingani?
Akukho nto. Kungaphezulu kwamawaka amabini abantu ubungakanani belizwe aluyi kubangela ukuba kubekho umda- into ebalulekileyo kubungakanani besampula. Yiyo loo nto ukhetho lwelizwe kunye nokhetho lwesixeko luya kuba nenani elifanayo labantu abaphendulayo.
Umgangatho woxanduva utshintsha njani umda wemposiso?
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.
API — sebenzisa le calculator ukusuka kwikhowudi
Nceda le khadi lemali njengendawo esemva ye-JSON ekhululekileyo - akukho qhosha lifunekayo. Thumela amaxabiso endawo ezantsi njengeparameter yombuzo okanye i-JSON. Nantoni na oyenzayo isebenzisa okungagqibekanga okufanayo eli phepha ligqityiwe ngaphambili; iparameter engaziwayo yi 400, ayikho i zero ekhululekileyo. Funda i-API epheleleyo →
Incopho yesiphelo
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);Results are estimates for general guidance only, not financial, medical or tax advice.