Variance, standard deviation and coefficient of variation
Measure spread with the squared distances from the mean: variance, standard deviation, and the coefficient of variation for comparing spreads in different units.
- UK: Year 12
- France: grade 10
- Iran: grade 10
- Afghanistan: grade 10
- Syria: grade 11
- Palestine: grade 8
- Russia: grade 10
Guide
The mean deviation adds the distances from the mean. The variance squares them first: S² = Σ(x − x̄)² ÷ n. Squares are never negative, so the distances cannot cancel each other, and far values count more.
There is a shorter way: S² = Σx² ÷ n − x̄². Add the squares of the values, divide by n, then subtract the square of the mean. The standard deviation is S = √(variance), which is back in the units of the data (the variance is in square units).
To compare the spread of two kinds of data (heights in cm and weights in kg) use the coefficient of variation: CV = S ÷ x̄ × 100%. It says how big the spread is compared with the mean, and it has no unit.