Standard Deviation Calculator

Sample or population • Raw list or value:count

Inputs

Numbers

Separators: comma, space, newline, semicolon. Frequency format: value:count, where count must be a positive integer.

Standard deviation type Use sample standard deviation (n−1)

Turn this off to calculate population standard deviation using n.

Options Show sorted preview

Large datasets are previewed in compressed form.

Action

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Use this Standard Deviation Calculator to calculate sample or population standard deviation, variance, and mean from a numeric dataset.

Calculation Method

Sample standard deviation:

s = √[Σ(x − x̄)² ÷ (n − 1)]

Population standard deviation:

σ = √[Σ(x − μ)² ÷ N]

Standard deviation is the square root of variance.

Example

For:

2, 4, 4, 4, 5, 5, 7, 9

The mean is 5 and the sum of squared deviations is 32.

Population SD = √(32 ÷ 8) = 2

Sample SD = √(32 ÷ 7) ≈ 2.14

Important Note

Use sample standard deviation when the data represent a sample from a larger population. Standard deviation is sensitive to extreme values and does not by itself show that data follow a normal distribution.

Source

OpenStax Introductory Statistics 2e — Measures of the Spread of the Data

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