Let be observations.

MATHEMATICS · Multi-part · CBSE · Mathematics · Statistics · Statistics

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.