Standard Deviation Calculator
Standard deviation measures how far the numbers spread from their mean — the dispersion of the data. Enter your values and pick population or sample to get the standard deviation, variance and mean.
Your numbers
Result
- Variance
- 4
- Mean
- 5
- Count
- 8
| Step | Value |
|---|---|
| Count | 8 |
| Mean | 5 |
| Variance (÷ n) | 4 |
| Standard deviation | 2 |
How it is calculated
First the mean. Then, for each value, the squared difference from the mean; add those up and divide by n (population) or n−1 (sample) to get the variance. The standard deviation is the square root of the variance. For 2, 4, 4, 4, 5, 5, 7, 9 (population): mean 5, variance 4, standard deviation 2.
Population or sample?
Use population (÷ n) when your data is the entire group. Use sample (÷ n−1) when it is a sample drawn from a larger group — dividing by n−1 (Bessel's correction) offsets the tendency of a sample to underestimate the true spread.
What the number tells you
A low standard deviation means values cluster near the mean; a high one means they are spread out. In a normal distribution, about 68% of values fall within one standard deviation of the mean and 95% within two — the basis of many statistical tests and confidence intervals.
Frequently asked questions
Sources
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