Standard Deviation Calculator — Population & Sample
Use this free standard deviation calculator to find the standard deviation, variance and full statistical summary of any dataset. Choose between population standard deviation (σ) for complete datasets or sample standard deviation (s) for subsets of data.
Standard Deviation Calculator
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What Is Standard Deviation?
Standard deviation measures how spread out numbers are in a dataset — how much individual values differ from the mean. A small standard deviation means values are clustered closely around the mean. A large standard deviation means values are widely spread.
Population vs Sample Standard Deviation
Population standard deviation (σ) — use when you have data for an entire population. Divides by n.
Sample standard deviation (s) — use when your data is a sample taken from a larger population. Divides by n−1. This is the more common version used in research and statistics.
If you’re unsure which to use — choose Sample for research data and Population when you have the complete dataset.
The 68-95-99.7 Rule
In a normal distribution approximately 68% of values fall within 1 standard deviation of the mean, 95% within 2 standard deviations and 99.7% within 3 standard deviations. The calculator shows these exact ranges for your dataset.
FAQs
What does standard deviation tell you?
It tells you how spread out your data is. A low standard deviation means most values are close to the mean. A high standard deviation means values are widely dispersed.
What is the difference between standard deviation and variance?
Variance is the average squared difference from the mean. Standard deviation is the square root of variance — it’s expressed in the same units as the original data which makes it easier to interpret.
Should I use population or sample standard deviation?
Use population when you have data for an entire group. Use sample when your data is a subset of a larger population — which is most common in research and statistics.
What is a good standard deviation?
There is no universal answer — it depends entirely on the context and scale of your data. A standard deviation of 5 is tiny for house prices but enormous for exam scores out of 20.
Is this calculator free?
Yes completely free with no sign-up needed.