Chapter 3.2, Problem 27P

Brain Teaser: Sum of Squares If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The sample size is n. Fill in the details for the following steps.

$\begin{array}{l}\sum {(}^x=\sum x^2-2\bar{x}\sum x+n{\bar{x}}^2\\ =\sum x^2-2n{\bar{x}}^2+n{\bar{x}}^2\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}=\sum x^2-\frac{{(\sum x)}^2}{n}\end{array}$