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Standard Deviation Calculator — Sample & Population Variance with Steps

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Dataset Paste directly from a spreadsheet column. You can also use value:frequency shorthand such as 10:3. Invalid tokens are rejected rather than ignored.Variance / standard deviation basis Displayed precision

Calculated result

Sample SD 2.1381

Variance: 4.5714 · Mean: 5 · n: 8

Sum: 40 · Sum of squared deviations: 32

Population SD: 2 · Sample SD: 2.1381

Standard error: 0.7559

Coefficient of variation: 42.7618%

Tukey outliers: none

Deviation table

x	x − mean	(x − mean)²	z
2	-3	9	-1.4031
4	-1	1	-0.4677
4	-1	1	-0.4677
4	-1	1	-0.4677
5	0	0	0
5	0	0	0
7	2	4	0.9354
9	4	16	1.8708

Show the working

1. Mean = 40 ÷ 8 = 5.
2. For each value, calculate x − mean and square that deviation; Σ(x−mean)² = 32.
3. Sample variance = Σ(x−x̄)² ÷ (n−1) = 4.5714.
4. Standard deviation = √4.5714 = 2.1381.

Choose Sample when these observations are a subset used to estimate a larger population; choose Population when the dataset contains every observation in the population you mean to describe.

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