Free Variance Calculator
Calculate the sample and population variance to measure how spread out values are from the mean.
Sample Variance
2.5000
Population Variance2.0000
Mean6.0000
Sample Variance vs Value 1
How to Calculate Variance
Population Variance
sigma^2 = Sum of (xi - mean)^2 / N
Sample Variance
s^2 = Sum of (xi - mean)^2 / (n - 1)
Variance measures the average squared distance of each data point from the mean. The sample variance divides by (n-1) instead of n to correct for the bias introduced by estimating the population mean from the sample (Bessel's correction).
Example Calculation
Find the variance of 4, 8, 6, 5, 7.
- 01Mean = (4 + 8 + 6 + 5 + 7) / 5 = 30 / 5 = 6
- 02Squared deviations: (4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (5-6)^2=1, (7-6)^2=1
- 03Sum of squares = 4 + 4 + 0 + 1 + 1 = 10
- 04Population Variance = 10 / 5 = 2
- 05Sample Variance = 10 / 4 = 2.5
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.