Mean and Standard Deviation Calculator
Enter a list of numbers to instantly calculate the mean, variance, and standard deviation, with a chart showing each value against the mean.
Enter Your Data
Results
Count (n)
8
Mean
18.0000
Variance (population)
24.0000
Standard Deviation (population)
4.8990
Min
10
Max
23
Data Points vs Mean
How the Mean and Standard Deviation Calculator Works
This calculator takes a list of numbers and computes the mean (average), variance, and standard deviation, which measure how spread out the values are. Enter numbers separated by commas, spaces, or new lines, choose whether your data is a full population or a sample, and the tool returns the summary statistics along with a chart plotting every value against the mean and one standard deviation band.
Formula
Mean = sum of values / count. Population variance = sum of (value - mean)^2 / n. Sample variance = sum of (value - mean)^2 / (n - 1). Standard deviation = square root of variance.
Example
For the data set 10, 12, 23, 23, 16, 23, 21, 16, the mean is 18. The sample standard deviation is about 5.24, meaning most values fall within roughly 5.24 of the mean.
Limitations
Standard deviation assumes numeric, reasonably clean data. A single extreme outlier can inflate the result, so review the data set for entry errors before relying on the output. Use the sample formula when your numbers are a subset of a larger population, and the population formula when your numbers are the entire group.
How to use the result responsibly
- Check that every input uses the unit and time period shown beside the field.
- Compare the result with the worked example and formula above.
- For financial, tax, health, or legal decisions, confirm current rules with a qualified professional or the relevant authority.
Frequently Asked Questions
Should I use population or sample standard deviation?
Use the sample standard deviation (dividing by n - 1) when your data is a sample drawn from a larger population, which is the more common case in statistics homework and surveys. Use the population version only when your list truly contains every member of the group you care about.
Why is standard deviation useful?
Standard deviation shows how tightly or loosely data clusters around the mean. A small standard deviation means values are close together, while a large one means the data is more spread out.
Can standard deviation be negative?
No. Standard deviation is a square root of a sum of squared values, so it is always zero or positive.
Editorially reviewed September 22, 2026. Read our calculation methodology and editorial policy.