How to calculate standard deviation
- Find the mean: add the numbers and divide by how many there are (n).
- Subtract the mean from each number and square the result.
- Add the squares up and divide by n − 1 for a sample, or by n for a population. That’s the variance.
- Take the square root of the variance.
s = √( Σ(x − x̄)² ÷ (n − 1) )
Example
For 4, 8, 15, 16, 23 and 42 the mean is 108 ÷ 6 = 18. The squared differences add up to 910, so the sample variance is 910 ÷ 5 = 182 and the sample standard deviation is 13.49.
Frequently asked questions
Should I use sample or population standard deviation?
Use population when your numbers are the whole group you care about, such as every student in one class. Use sample when they're a sample from a bigger group and you want to estimate that group's spread, such as 50 customers surveyed out of thousands. Sample divides by n − 1 instead of n, which makes it slightly larger.
What does the standard deviation tell me?
How spread out the numbers are around the mean. A small standard deviation means most values are close to the average; a large one means they're scattered. For data with a bell-shaped spread, about 68% of values fall within one standard deviation of the mean, and 95% within two.
How do I enter my numbers?
Paste or type them separated by commas, spaces, semicolons or new lines. You can paste a column straight from a spreadsheet.
What is variance?
The standard deviation squared: the average of the squared distances from the mean. It's used in statistics formulas, but the standard deviation is easier to read because it's in the same units as your data.
