2, 4, 4, 4, 5, 5, 7, 9 as a population
Mean 5, squared deviations total 32, variance 32 ÷ 8 = 4, standard deviation 2.
Standard Deviation Calculator
Calculate the standard deviation, variance and mean of a data set, for a sample or a population.
Result
Enter your values and select Calculate to see the result.
Runs in your browser — nothing you enter is sent to a server.
How the Standard Deviation Calculator works
Paste or type your numbers, separated by commas, spaces or new lines, and choose sample or population. Standard deviation measures how spread out the values are around their mean: small when they cluster, large when they're scattered. The working shows each step.
Formula
s = √(Σ(x − x̄)2 ÷ (n − 1))
Where:
- x̄
- The mean
- n
- How many values
For a population, divide by n instead of n − 1. The variance is the value before the square root.
Examples
The same numbers as a sample
32 ÷ 7 = 4.5714, standard deviation 2.1381.
Frequently asked questions
Sample or population?
Population when your data is the whole group you care about (every student in the class); sample when it's part of a bigger group (a survey). Most real data is a sample.
Why divide by n − 1 for a sample?
A sample's values sit closer to their own mean than to the true population mean, so dividing by n would underestimate the spread. This is Bessel's correction.
What does a standard deviation of 0 mean?
Every value is the same, so there's no spread at all.
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