Standard deviation calculator

Calculate population or sample standard deviation, with the mean, variance and denominator used in the calculation.

Result

Enter your data and run the tool. Your result will appear here.

From variance to square root

Follow the steps through to the square root of the variance.

The values you enter stay on this page. Reloading or closing it clears them.

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How to use the tool

Fill in these fields: Numbers (whitespace, ; or newlines), Dataset type.
Select “Calculate” to obtain the result.
Follow the steps through to the square root of the variance.
The line marks the mean. Each dot represents an observation and the segment shows its deviation. For long series the chart shows up to 12 observations, while the calculation uses them all.

Method and principles

Formula

σ = \sqrt{\frac{Σ {(x_{i} - μ)}^{2}}{n}}

Standard deviation is the square root of variance: σ=√[Σ(x−μ)²/n], or s=√[Σ(x−x̄)²/(n−1)] for a sample.

Sample (divide by n−1)

s = \sqrt{\frac{Σ {(x_{i} - x̄)}^{2}}{n - 1}}

Worked example

For 2; 4; 4; 4; 5; 5; 7; 9, the mean is 5 and the population standard deviation is 2.

Variance uses squared units. If the variance is 4 m², the standard deviation is 2 m, in the original unit.

Practical example

Input

Numbers (whitespace, ; or newlines): 2; 4; 4; 4; 5; 5; 7; 9
Dataset type: Population (divide by n)

Result

σ = \sqrt{\frac{32}{8}} = \sqrt{4} = 2

Limits and interpretation

Sample calculations need at least two observations. Standard deviation has the same units as the data. It is not a confidence interval and does not imply normally distributed data.

Result details

Result details
Parameter	Value
Observations	8
Arithmetic mean	5
Variance	4
Standard deviation	2
Divisor	8

Limits and checks

Limits and checks
Parameter	Value
Numbers (whitespace, ; or newlines)	≤ 200000 characters

Standard deviation calculator

Set your data

Result

From variance to square root

How to use the tool

Method and principles

Formula

Sample (divide by n−1)

Worked example

Practical example

Limits and interpretation

Result details

Limits and checks

Favorites

Standard deviation calculator

Set your data

Result

How to use the tool

Method and principles

Formula

Sample (divide by n−1)

Worked example

Practical example

Limits and interpretation

Result details

Limits and checks

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