What is the formula for variance?

Variance is a measure of how much values in a data set deviate from the mean of that data set. The correct formula for population variance is represented by the formula ( \sigma² = \Sigma(xᵢ - μ)² / N ).

In this formula, ( σ² ) represents the population variance, ( Σ ) indicates the summation, ( xᵢ ) represents each individual observation in the data set, ( μ ) is the population mean, and ( N ) is the total number of observations in the population. The expression ( (xᵢ - μ)² ) calculates the squared difference between each observation and the mean, and the summation aggregates these squared differences. Finally, dividing this total by ( N ) provides the average of the squared deviations, which is precisely the definition of variance.

In contrast, the other formulas listed focus on variations of this concept. For instance, the formula involving ( n ) in one choice refers to sample variance, which divides by ( (n-1) ) to account for sample bias, while another option simply calculates the square root of the variance, giving the standard deviation rather than the variance itself. By understanding the