Math

Standard Deviation

Calculate mean, variance, and standard deviation for a data set.

Sample standard deviation

2.4495

Mean: 15.5000 Ā· n = 8

Variance (ĻƒĀ²)

6.0000

Mean

15.5000

Count

8

Min

12.0000

Max

19.0000

Population Ļƒ

2.2913

Distribution around the mean

Ī¼ 15.50

Shaded band = mean Ā± 1Ļƒ (13.05 to 17.95). About 68% of a normal distribution falls in this range.

Learn more

How this calculator works and what to know before using it

What this calculator does

Computes mean, variance, and standard deviation for a data set using sample or population formulas.

Understanding your result

Standard deviation measures spread around the mean. A low value means data points cluster tightly; a high value means they are more dispersed.

How to use it

  1. Paste or type your data (comma, space, or line separated).
  2. Choose sample (n āˆ’ 1) or population (N) deviation.
  3. View mean, standard deviation, variance, min, and max.

Formula used

Sample and population standard deviation

Sample: s = āˆš(Ī£(xįµ¢ āˆ’ xĢ„)Ā² / (n āˆ’ 1)) Ā· Population: Ļƒ = āˆš(Ī£(xįµ¢ āˆ’ Ī¼)Ā² / N)

Source. Both forms take the square root of the average squared distance from the mean. The NIST/SEMATECH e-Handbook defines the standard deviation with a divisor of N āˆ’ 1, which is the sample form on this page. The population form divides by the number of values. NIST/SEMATECH e-Handbook, standard deviation.

Updated November 1, 2026

Example

12, 15, 18, 14, 16 ā†’ mean 15, sample standard deviation ā‰ˆ 2.24.

Good to know

  • Use sample deviation when data is a subset of a larger population.
  • Use population deviation when you have the complete data set.

Common questions

When should I use sample vs population standard deviation?
Use sample (nāˆ’1) when your data is a sample from a larger group. Use population (N) when you have every value in the group.
What does a high standard deviation mean?
Values vary widely from the average. A low standard deviation means most values are close to the mean.

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