Question

Find the mean and variance for the first 10 multiples of 3.

Answer 1

$x=3,6,9,12,15,18,21,24,27,30$

$\therefore \sum x=3+6+9+12+15+18+21+24+27+30$

= $165$

$n=10\therefore \text{Mean}\left(\overline{x}\right)=\frac{165}{10}=16.5$

$\sum x^2=(3{)}^2+(6{)}^2+(9{)}^2+(12{)}^2+(15{)}^2+(18{)}^2+(21{)}^2+(24{)}^2+(27{)}^2+(30{)}^2$

=$9+36+81+144+225+324+441+576+729+900$

=$3465$ $\text{Variance}={\sigma }^2=\frac{N\sum x^2-(\sum x{)}^2}{N^2}$

= $\frac{10\times 3465-(165{)}^2}{(10{)}^2}$

= $\frac{3465-27225}{100}$

= $\frac{7425}{100}=74.25$