Standard deviation
Compute the population or sample standard deviation and variance of a list; 2, 4, 4, 4, 5, 5, 7, 9 has a population SD of 2.
- Runs in your browser
- No upload
- Instant result
Assumptions & formula
Formula and assumptions
σ²=M₂/n; s²=M₂/(n−1); SD=√variance
Results
Enter values and press Calculate to see the result here.
How to use this calculator
- Set inputs and units
Choose population or sample and paste the numeric observations. Sample mode needs at least two values.
- Calculate
Check this worked example: 2,4,4,4,5,5,7,9; population → mean5, variance4, SD2
- Results
Variance is in squared input units. The standard deviation goes back to the original unit and is never negative.
Questions and limits
Why do sample and population differ?
Population divides the squared deviations by n, and sample divides by n−1. For the same data that isn't constant, the sample SD is larger.
Which input errors should I correct?
Check decimal points, missing entries and extreme scales. A precision limit that is reported does not mean the variance is zero.
What does this calculation leave out?
Unweighted spread of at most 1,000 values. No normality test, and no guarantee that ±one SD contains a particular proportion.