Question

The mean of $30$ scores is $18$ and their standard deviation is $3$. Find the sum of all the scores and also the sum of the squares of all the scores

Answer 1

The number of scores $=n=30$
The mean of scores $=\overline{x}=18$
We know that, sum of scores $=\sum x=18\times 30=540(\because \overline{x}=\frac{\sum x}{n})$
$\therefore$ Sum of all scores $=540$
Standard deviation of $30$ scores $=\sigma =3$
$\therefore {\sigma }^2=\frac{\sum x^2}{n}-{\left(\frac{\sum x}{n}\right)}^2\therefore \frac{\sum x^2}{30}-{18}^2=9$
$\frac{\sum x^2}{30}=9+324$
$\therefore \sum x^2=333\times 30=9990$
$\therefore$ sum of squares of all the scores $=9990$.