Standard Deviation Calculator
Enter a list of numbers and choose whether it is a sample or a whole population. The calculator shows the mean, each value’s deviation from the mean, the squared deviations, their sum, the variance and finally the standard deviation, so you can follow or check every step of the working.
How to use the Standard Deviation Calculator
- Type or paste your values.
- Choose sample (n − 1) or population (N).
- Read the standard deviation and variance.
- Follow the deviation table, or download it as CSV.
Features
- Sample and population formulas
- Step-by-step deviation table
- Sum of squares, variance and standard deviation
- Copy summary and CSV download
Benefits
- Learn how standard deviation is built up
- Check hand calculations line by line
- Results update as you type
Frequently asked questions
Why divide by n − 1 for a sample?
Using n − 1 (Bessel’s correction) makes the sample variance an unbiased estimate of the population variance, because a sample tends to sit closer to its own mean than to the true mean.
What does standard deviation tell me?
It measures how spread out values are around the mean, in the same units as the data. A small value means the data is tightly clustered.
Why does the deviation column add up to zero?
The deviations from the mean always sum to zero, which is why they are squared before being added.
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