Free Standard Deviation Calculator
Calculate the sample and population standard deviation to quantify how spread out values are.
Sample Standard Deviation
1.581139
Population Standard Deviation1.414214
Mean6.0000
Sample Standard Deviation vs Value 1
How to Calculate Standard Deviation
Formula
Population SD (sigma) = sqrt( Sum of (xi - mean)^2 / N )
Sample SD (s) = sqrt( Sum of (xi - mean)^2 / (n - 1) )
Standard deviation is the square root of the variance and is expressed in the same units as the original data. About 68% of data in a normal distribution falls within one standard deviation of the mean.
Example Calculation
Find the standard deviation of 4, 8, 6, 5, 7.
- 01Mean = 30 / 5 = 6
- 02Squared deviations: 4, 4, 0, 1, 1
- 03Sum of squares = 10
- 04Sample SD = sqrt(10 / 4) = sqrt(2.5) ≈ 1.5811
- 05Population SD = sqrt(10 / 5) = sqrt(2) ≈ 1.4142
Frequently Asked Questions
Learn More
Understanding the Normal Distribution
Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.