Sample or population — which do I need?

If your data is a sample drawn from a bigger group, use the sample figure. Population SD is only correct when you have measured every member.

Why square the deviations?

Deviations above and below the mean would otherwise cancel out to zero. Squaring makes them all positive and penalises larger deviations more heavily.

What is a high standard deviation?

It only means anything relative to the mean. Dividing SD by the mean gives the coefficient of variation, which allows comparison between data sets of different scales.

Standard Deviation Calculator

Standard deviation measures how far values typically sit from the mean. This calculator returns both the population and the sample figure, since choosing the wrong one is a common mistake.

Fill in the fields above and select Calculate to see your result and the full working.

Formula used

s = √(Σ(x − x̄)² ÷ (n − 1)) for a sample; σ = √(Σ(x − μ)² ÷ n) for a whole population

How to use this calculator

Enter every value in your data set.
Use the sample figure when your numbers are a subset of a larger group — this is the usual case.
Use the population figure only when the data covers every member of the group you care about.

Example calculation

For 4, 8, 6, 5, 3, 9, 7:

Mean = 6

Squared deviations sum to 28

Sample variance = 28 ÷ 6 = 4.667 → s = 2.16

Population variance = 28 ÷ 7 = 4 → σ = 2.

What does this result mean?

Standard deviation is in the same units as your data, which makes it directly interpretable: a mean of 6 with an SD of 2 means most values sit roughly between 4 and 8. For approximately normal data, about 68% of values fall within one standard deviation of the mean and about 95% within two. Dividing by n − 1 for samples corrects a bias that would otherwise understate the true spread.

Frequently asked questions

Sample or population — which do I need?: If your data is a sample drawn from a bigger group, use the sample figure. Population SD is only correct when you have measured every member.
Why square the deviations?: Deviations above and below the mean would otherwise cancel out to zero. Squaring makes them all positive and penalises larger deviations more heavily.
What is a high standard deviation?: It only means anything relative to the mean. Dividing SD by the mean gives the coefficient of variation, which allows comparison between data sets of different scales.

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