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Standard Deviation Calculator

Find the standard deviation and variance of numbers.

Separated by commas, spaces or new lines.

The numbers are

Most data is a sample.

Result

Standard deviation (sample, s)

2.138089935

Variance
4.571428571
Mean
5
Count
8
Standard error of the mean
0.755928946
Population standard deviation
2
Show stepsHide steps
  1. Mean = 40 ÷ 8 = 5
  2. Sum of squared differences from the mean = 32
  3. Variance = 32 ÷ (8 − 1) = 4.571428571
  4. Standard deviation = √4.571428571 = 2.138089935

Runs on your device.

Questions

Sample or population?

Use population when your numbers are every member of the group you care about. Use sample when they are some of a larger group, which is most data. The sample formula divides by n − 1 to avoid underestimating the spread.

What does standard deviation mean?

How far values typically are from the mean, in the same units as the data. For roughly bell-shaped data, about 68% of values lie within one standard deviation of the mean.

What is the standard error?

The standard deviation divided by the square root of the count: how much the sample’s mean would vary between samples.

Is it free? Do I need an account?

It is free to use and there is nothing to sign up for. There are no watermarks and no daily limits.

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