Variance Calculator — Formula
## 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).
### 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).
Esempio Risolto
Find the variance of 4, 8, 6, 5, 7.
- Mean = (4 + 8 + 6 + 5 + 7) / 5 = 30 / 5 = 6
- Squared deviations: (4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (5-6)^2=1, (7-6)^2=1
- Sum of squares = 4 + 4 + 0 + 1 + 1 = 10
- Population Variance = 10 / 5 = 2
- Sample Variance = 10 / 4 = 2.5