Standard Deviation Calculator
Calculate standard deviation, variance, mean, and more from your data set. Supports both population and sample calculations.
Population SD (ฯ)
2.0000
Sample SD (s)
2.1602
Mean
6.0000
Count
7
Population Variance
4.0000
Sample Variance
4.6667
Formula
ฯ = โ(ฮฃ(xแตข - ฮผ)ยฒ / N) for population โ s = โ(ฮฃ(xแตข - xฬ)ยฒ / (n-1)) for sampleUnderstanding Standard Deviation
Standard deviation measures the amount of variation in a data set. A low standard deviation means data points tend to be close to the mean, while a high standard deviation indicates the data is spread out over a wider range.
The 68-95-99.7 Rule
For normal distributions: ~68% of data falls within 1 SD of the mean, ~95% within 2 SDs, and ~99.7% within 3 SDs.
Frequently Asked Questions
Population vs sample standard deviation?
Population SD divides by N (all data). Sample SD divides by N-1 (Bessel's correction) to account for estimating from a subset.
What does standard deviation tell you?
It measures how spread out values are from the mean. Low SD means data is clustered near the mean; high SD means it's widely spread.