Question

A population of n = 6 scores has sx = 12 and sx2 = 54. what is the value of ss for this population?

Answer 1

The sum of squares of a population is given by
$SS=\Sigma(x-\bar{x})^2$
and the standard deviation is given by
$SX= \sqrt{ \frac{\Sigma(x-\bar{x})^2}{n-1} }$

Given that SX = 12, i.e.
$\sqrt{ \frac{\Sigma(x-\bar{x})^2}{6-1} }=12 \\ \\ \Rightarrow \frac{\Sigma(x-\bar{x})^2}{5}=12^2=144 \\ \\ \Rightarrow\Sigma(x-\bar{x})^2=144\times5=720$

Therefore, SS = 720