Sample Size for a Mean

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Calculate

Example: to estimate the average wait in a queue, a pilot study pointed to a standard deviation of 15 minutes. How many people should be observed to be off by at most 3 minutes, with 95% confidence? Change the values to work out your own case.

Confidence (%) Standard deviation σ Margin of error E

Step by step

What each term means

Sample Size (n): How many observations are needed to estimate the mean with the requested margin of error and confidence. The result is always rounded up.
Squared Critical Value (z²): It comes from the confidence level: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%. More confidence calls for more observations.
Variance (σ²): How much the data vary. It usually comes from a pilot study or earlier research; the more scattered the data, the larger the sample.
Squared Margin of Error (E²): The largest accepted gap between the sample mean and the true one, in the units of the data. Because it is squared, halving it quadruples the sample.