Sum of Squares vs Variance

The sum of squares adds up how far every value falls from the mean after squaring each gap, so positive and negative deviations can no longer cancel. You compute $\text{SS} = \sum (x_i - \bar{x})^2$, where $\bar{x}$ (x-bar) is the mean. For the data 2, 4, 6, 8 the mean is 5, the squared deviations are 9, 1, 1, and 9, and the sum of squares is 20. Dividing that 20 by $n - 1 = 3$ gives the sample variance $s^2 \approx 6.667$, and its square root is the sample standard deviation.

Variance quantifies spread from the squared deviations, so it is always non-negative. The sample variance is $s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2$, where $x_i$ are the values, $\bar{x}$ (x-bar) is the mean, and $n$ is the number of values. For example, data tightly packed around the mean have a small variance. Because the deviations are squared, variance is measured in squared units, and its square root is the standard deviation.