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Math & Statistics

Variance Calculator

Calculate the mean, sample variance, and population variance for a set of 5 numbers.

Inputs

-10,00010,000
-10,00010,000
-10,00010,000
-10,00010,000
-10,00010,000

Calculation Results

Mean (Average)

20

Population Variance (σ²)

50

Sample Variance (s²)

62.5

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Formula & Mathematical Explanation

σ2=∑(xi−μ)2N,s2=∑(xi−xˉ)2n−1\displaystyle \sigma^2 = \frac{\sum (x_i - \mu)^2}{N}, \quad s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}

Variance measures the dispersion of a dataset. Population variance divides the sum of squared deviations from the mean by N, while sample variance divides by n - 1.