Chapter 2 - Methods for Describing Sets of Data - Exercises 2.44 - 2.47 - Learning the Mechanics - Page 50: 2.46a

$11.2$

Recall that it was computed that $\displaystyle \sum x^{2}$=$5^{2}+1^{2}+3^{2}+2^{2}+1^{2}=40$ and $\displaystyle \left(\sum x\right)^{2}=(5+1+3+2+1)^{2}=144.$ So, \begin{align*} \displaystyle \sum x^{2}-\displaystyle \frac{\left(\sum x\right)^{2}}{5}&=40-\displaystyle \frac{144}{5}\\ &=\displaystyle \frac{56}{5}\\ &=11.2\end{align*}