๐ Standard Deviation Calculator
Calculate standard deviation and variance
How Standard Deviation Is Calculated
Formula
ฯ = โ(ฮฃ(xแตข โ ฮผ)ยฒ / N)
- 1Enter your data set as comma-separated values.
- 2The mean (average) of all values is calculated.
- 3Each value's deviation from the mean is found and squared.
- 4The squared deviations are averaged (divided by N for population, Nโ1 for sample).
- 5The square root of that average gives the standard deviation.
About Standard Deviation Calculator
Calculate the standard deviation, variance, and mean of a data set. Supports both population and sample standard deviation with step-by-step formulas shown.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation divides by N (the total number of values). Sample standard deviation divides by Nโ1 to correct for bias when estimating from a sample. Use sample when your data is a subset of a larger group.
What does a high standard deviation mean?
A high standard deviation means the data points are spread far from the mean, indicating high variability. A low standard deviation means the data is clustered closely around the mean.
How is variance related to standard deviation?
Variance is the square of the standard deviation. Standard deviation is more commonly used because it is in the same units as the original data, making it easier to interpret.