Variance (s² σ²)

How to read it

OpenStax’s Introductory Statistics: “The symbol σ² represents the population variance; the population standard deviation σ is the square root of the population variance. The symbol s² represents the sample variance; the sample standard deviation s is the square root of the sample variance.” The squared symbol says what variance is, the standard deviation squared, which is why it has no letter of its own. Because the distances are squared, the variance is not in the same units as the data; OpenStax notes that taking the square root, to get the standard deviation, solves that. NIST’s Engineering Statistics Handbook adds that squaring gives more weight to values far from the mean: a point 2 units from the mean adds 4 to the sum, and a point 10 units away adds 100.

Also searched as: s² σ², sigma squared, s squared, variance symbol.

Dividing by N or by n − 1

For a whole population, OpenStax divides the sum of the squared deviations by N, the number of items in the population. For a sample it divides by n − 1, one less than the number of items in the sample. OpenStax’s reason is that the sample variance is an estimate of the population variance, and dividing by n − 1 gives a better estimate. NIST’s handbook puts N − 1 in the same place in its definition of s², where its N is the number of values in the sample (see Sample size (n N)).

Look-alikes

σ² is the small sigma σ squared, not the capital Σ of summation. The small raised 2 is the superscript two (U+00B2), which Unicode also names “squared”. The coefficient of determination R² is a square too, but of a correlation coefficient, and it is not a variance.