A poll of 1,000 people has a margin of error of ±3.1% at 95% confidence.
Doubling sample size reduces margin of error by √2 — not by half.
Use this statistical calculator when you need a rigorous, reportable result — not a rough estimate. The formula is standard, but manual computation on large datasets introduces errors that undermine any subsequent analysis.
A frequent mistake is computing statistics on a dataset without checking for data entry errors, outliers, or missing values. A single transcription error in a small dataset can shift the mean and standard deviation substantially. Always verify the input data before interpreting results.
A teacher calculates the class average and standard deviation for an exam: mean 64%, SD 18%. The high SD suggests a wide spread of performance levels — indicating the class may need differentiated support rather than a single revision strategy.
MoE = z × √(p(1-p)/n). For 95% confidence (z=1.96), 50% response rate, n=1000: ±3.1%.