Standard Deviation

How spread out are your numbers?

Paste in a list and get both population and sample standard deviation, so you're not guessing which one applies.

Count
Mean

Population

Variance
Standard deviation

Sample

Variance
Standard deviation

Last updated 23 August 2026

Population or sample — which one?

If your numbers are the entire group you care about — every test score in one specific class — use population standard deviation. If your numbers are a sample standing in for a bigger group you can't fully measure — a hundred customers representing all customers — use sample standard deviation. The sample version divides by one less, which corrects for the fact that a smaller subset tends to understate the true spread.

Reading the number

Standard deviation is in the same units as your original data, which is what makes it more useful to read than variance directly. A small value means the numbers sit close to the mean; a large one means they're spread wide. It's the standard way to describe consistency — in test scores, manufacturing tolerances, or anything else where "how much do these vary" matters as much as the average itself.

Common questions

Should I use population or sample standard deviation?

Use population if your numbers are the entire group you care about — every student in a class, every day last month. Use sample if your numbers are a subset standing in for a larger group you're trying to estimate. When unsure, sample is the more common and more cautious choice.

What does a high standard deviation mean?

The values are spread out further from the mean. A low standard deviation means they cluster tightly around it. Two data sets can have the same mean and look completely different once you see the spread.

What's the difference between variance and standard deviation?

Variance is the average of the squared differences from the mean. Standard deviation is just the square root of variance, which brings it back into the same units as the original numbers — that's why standard deviation is usually the more useful figure to read.

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