Standard Deviation & Variance Calculator
Mean, variance, and standard deviation of a data set — population or sample.
Every calculation runs locally in your browser.
Standard deviation
2
Variance
4
Mean
5
Min
2
Max
9
n = 8, sum = 40
For informational and educational purposes only — not professional or technical advice, and not a substitute for consulting a qualified professional about your specific situation. TrueMeasureKit is not liable for decisions made based on these results. See our Terms of Service.
Population vs. sample — why the divisor changes
If your numbers are the entire group you care about — every student in a class, every day in a month — divide by n (population variance). If your numbers are a sample meant to estimate a larger population — a survey of 50 customers standing in for all customers — divide by n − 1 instead (Bessel's correction). A sample's spread tends to slightly underestimate the true population's spread, since a sample is less likely to include extreme outliers; dividing by the smaller n − 1 inflates the estimate just enough to correct for that bias. Standard deviation is simply the square root of variance, which converts the units back from "squared" to the original scale of the data.
Frequently asked questions
Should I use population or sample standard deviation?
Use population if your data represents the entire group you care about. Use sample if your data is a subset used to estimate a larger population's variability — sample standard deviation divides by (n−1) instead of n, which slightly increases the result to correct for the smaller sample's tendency to understate true variability.