Standard Deviation Calculator

Sample and population standard deviation, variance and mean from a list of numbers.

Sample SD (s)

13.4907

Population SD (σ)

12.3153

18

Mean

151.6667

Variance (σ²)

6

Count

How it works

Standard deviation measures how spread out numbers are around the mean. Use sample SD (÷ n−1) for a sample, population SD (÷ n) for the whole population.

How it works

σ = √( Σ(x − mean)² ÷ N )

Standard deviation measures how spread out a set of numbers is around their average. A small standard deviation means the values cluster tightly near the mean; a large one means they are scattered widely. It is calculated by taking each value's distance from the mean, squaring it, averaging those squared distances (the variance), and taking the square root to return to the original units. The square root is why standard deviation is easier to interpret than variance. Use the population formula (dividing by N) when your data is the whole group, and the sample formula (dividing by N − 1) when it is a sample used to estimate a larger population. The distinction matters most on small datasets.

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Frequently asked questions

Sample vs population SD?

Sample SD divides by n−1 (for data from a sample); population SD divides by n (for the entire population).

What is variance?

The square of the standard deviation — the average squared distance from the mean.

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