How to use Standard Deviation Calculator
- Paste the numbers into Numbers to measure.
- Choose Population or sample, then set the decimal places.
- Tick Add the deviation table for each value and its distance from the mean.
- The spread updates as you change the numbers. Read the denominator used.
Example: Standard Deviation Calculator
Population standard deviation of 2, 4, 4, 4, 5, 5, 7 and 9.
Options
- Population or sample
- Population (divide by n) treats the list as the whole set. Sample (divide by n - 1) treats it as part of a larger set and needs two values.
- Add the deviation table
- Lists each value with its deviation from the mean and the squared deviation, for up to 50 values. Longer lists return the summary alone.
- How the numbers are separated
- Detect from the text takes the separator that appears most often; when none is found, spaces separate values.
Supported inputs and limits
Where your input is processed
This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.
Variance and standard deviation use different units
Squaring each distance from the mean is why variance comes out in squared units, so values in kilograms give a variance in kilograms squared. The standard deviation is its square root and returns to the input unit, which is why it is read beside the mean. The table prints the sum of squared deviations so the arithmetic can be followed.
Why the sample formula divides by n - 1
A sample stands in for a population not measured in full, and the sample mean is fitted to the sample itself. Dividing by the count alone understates the spread around the true mean, so the sample calculation divides by one less. The denominator is printed beside the answer, so the rule is visible.
Questions about Standard Deviation Calculator
Should I choose population or sample?
Population when the list is the whole set, sample when it is part of a larger set. The only difference is the denominator, n or n - 1.
Why is the sample standard deviation larger?
For 2, 4, 4, 4, 5, 5, 7 and 9 the population figures are variance 4 and standard deviation 2. Sample mode divides by 7, giving variance 4.571429 and standard deviation 2.13809.
Why is variance in different units from the input?
Each deviation is squared before averaging, so variance is in squared units. The standard deviation is its square root and returns to the input unit.
Can the standard deviation be zero?
Yes, when every value is identical. Every deviation is then zero, so the variance and the standard deviation are zero too.