Question:

The numbers form an arithmetic sequence: 4, 8, 12, . . . , 80. The mean is $\bar{x} = \frac{4 + 80}{2} = 42$. We calculate $\sum x_i^2 = 4^2 + 8^2 + \ldots + 20^2 = 45920$. The variance is $\sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2 = \frac{45920}{20} - 42^2 = 2296 - 1764 = 532$.