Minimum Sample Size Required Calculator – Estimating the Population Mean

Instructions: This calculator finds the minimum sample size required to estimate the population mean (\(\mu\)) within a specified margin of error. Please select type the the significance level (\(\alpha\)), the population standard deviation \(\sigma\) (or the approximated pop. standard deviation. If not known, the sample standard deviation can be used), and the required margin of error (E), and the solver will find the minimum sample size required:

Required Margin of Error (E)
Population St. Deviation (or an estimate)
Significance level (\(\alpha\))

Minimum Size Required for the Mean

More about the minimum sample size required to estimate the population mean so you can better interpret the results obtained by this solver: Often times we are interested in estimating a population parameter like the population mean, \(\mu\) within a certain range of precision.

Such precision is usually referred to as margin of error (MOE) .

How do you find the minimum sample size?

Provided that a desired margin of error is given, the population standard deviation \(\sigma\) is provided, and the significance level is specified, we can compute the minimum required sample size that will lead to a margin of error less than or equal to the one specified, by using the following formula:

\[n \ge \left( \frac{z_c \sigma}{E}\right)^2 \]

If you are dealing with a population proportion instead of a population mean, you should use instead our minimum required sample size calculator for proportions .

Why is 30 the minimum sample size?

That convention refers to a different situation: it refers to the usual minimum sample size required for the Central Limit Theorem to apply. This minimum sample size calculator computes the minimum sample size to achieved a certain specified interval width.

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