Standard Deviation Calculator
Population and sample standard deviation, variance and more.
Sample standard deviation
6.2105900341
7 values, mean 19.2857142857
Variance
38.5714285714
Mean
19.2857142857
Count
7
Coefficient of variation
32.20%
Population SD
5.749889085
Sample SD
6.2105900341
s = √(Σ(x − x̄)² ÷ (n − 1))
- Sample standard deviation divides by n − 1 (Bessel’s correction) because the mean was estimated from the data itself.
- About 68% of a normal distribution lies within one standard deviation of the mean — here, 13.0751242516 to 25.4963043198.
| Value | Deviation from mean | Squared deviation |
|---|---|---|
| 12 | -7.2857142857 | 53.0816326531 |
| 15 | -4.2857142857 | 18.3673469388 |
| 15 | -4.2857142857 | 18.3673469388 |
| 18 | -1.2857142857 | 1.6530612245 |
| 21 | 1.7142857143 | 2.9387755102 |
| 24 | 4.7142857143 | 22.2244897959 |
| 30 | 10.7142857143 | 114.7959183673 |
What does Standard Deviation Calculator do?
Calculate both population and sample standard deviation from a data set, along with variance, mean and the sum of squared deviations. The working is shown step by step, which makes it useful for checking homework as well as real analysis.
How to Use Standard Deviation Calculator
- 1Paste your dataAny list of numbers, in any common separator.
- 2Choose sample or populationBoth are calculated; pick which to highlight.
- 3Expand the workingSee each deviation squared if you need to show your method.
Key Features
- Both sample (n − 1) and population (n) results, clearly labelled
- Variance, mean and sum of squared deviations shown
- Step-by-step working table of each deviation and its square
- Coefficient of variation for comparing spread across different scales
Frequently Asked Questions
Should I use sample or population standard deviation?
Use sample (dividing by n − 1) when your data is a subset drawn from a larger group, which is almost always the case in research. Use population (dividing by n) only when you have measured every member of the group.
Why divide by n − 1 for a sample?
Because the sample mean is itself estimated from the data, which slightly understates the spread. Bessel’s correction compensates, giving an unbiased estimate of the population variance.
What does standard deviation actually tell me?
How far values typically sit from the mean. In a roughly normal distribution about 68% of values fall within one standard deviation of the mean and 95% within two.
What is the coefficient of variation?
Standard deviation divided by the mean, as a percentage. It lets you compare variability between data sets measured on completely different scales.
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