Calculate standard deviation, variance, mean, and more from a data set
How it works
Measures how spread out a set of numbers is around its mean. Low standard deviation means values cluster near the average; high standard deviation means they scatter widely.
σ = √( Σ(xᵢ − μ)² / N ) (population) s = √( Σ(xᵢ − x̄)² / (N − 1) ) (sample)
σ, spopulation / sample standard deviationxᵢeach value in the datasetμ, x̄mean of the datasetNnumber of values
- For roughly bell-shaped data: 68% of values are within 1σ, 95% within 2σ, 99.7% within 3σ (the 68-95-99.7 rule).
- Use sample SD (N − 1) when your data is a subset of a larger population. This is Bessel's correction.
Related Tools
Most Searched Today
Frequently Asked Questions
Step 1: find the mean. Step 2: subtract the mean from each value and square the result. Step 3: average those squared differences (that is variance). Step 4: take the square root.
Population SD divides by N (you have the whole population). Sample SD divides by N-1 (Bessel's correction) to account for bias when estimating the population from a sample. Use sample SD for most real-world datasets.
In a normal distribution: ~68% of values fall within 1 SD of the mean, ~95% within 2 SD, and ~99.7% within 3 SD. This is the empirical (68-95-99.7) rule.