Mathematics

Problem

Let

x_1, x_2, \dots , x_n

n

observations. a. Prove that

\displaystyle \sigma^{2}=\frac{1}{n}\sum_{i=1}^{n}x_i^{2}-\bar{x}^{2}

. (Symbols have their usual meanings.) b. Using the result from part (i), find the variance for the data set 3, 7, 8, 10.