EachCalculatorStandard Deviation Calculator
Calculate the standard deviation, variance, and mean of a list of numbers — both population and sample versions.
Mean
5
Population Std Dev
2
Sample Std Dev
2.14
Population Variance
4
Sample Variance
4.57
Count
8
How It Works
Variance
Variance measures how spread out values are from the mean: it's the average of each value's squared difference from the mean.
Population vs. sample
Population standard deviation divides by the total count (use when your data is the entire group you care about). Sample standard deviation divides by count minus one (use when your data is a sample used to estimate a larger population) — sample is always slightly larger.
Example Calculation
For the data set 2, 4, 4, 4, 5, 5, 7, 9: the mean is 5, the population standard deviation is 2, and the sample standard deviation is about 2.14.
Common Mistakes
- Using population standard deviation when the data is actually a sample of a larger group — this slightly underestimates the true spread.
- Confusing variance with standard deviation — standard deviation is the square root of variance, in the same units as the original data.
Frequently Asked Questions
- Should I use population or sample standard deviation?
- Use population if your numbers represent the entire group you're studying. Use sample if your numbers are a subset used to estimate a larger population — this is the more common case in surveys and experiments.
- What does a low vs. high standard deviation mean?
- A low standard deviation means values are clustered close to the mean. A high standard deviation means values are spread out over a wider range.