Question

Find the variance of first $10$ multiples of $3$.

• A. $70.15$
• B. $74.15$
• C. $73.15$
• D. $74.25$

Answer 1

Answer: (D)

Variance, ${\sigma }^2=\frac{\sum x_i^2}{n}-{\left(\bar{x}\right)}^2$
$=\left\{\frac{3^2+6^2+9^2+....+30^2}{10}-{\left(16.5\right)}^2\right\}$
$=\frac{3^2\times \left\{1^2+2^2+3^2+...+10^2\right\}}{10}-{\left(16.5\right)}^2$
$=\frac{9\times 10\times \left(10+1\right)\left(2\times 10+1\right)}{6\times 10}-{\left(16.5\right)}^2$
$=\left(\frac{9\times 10\times 11\times 21}{6\times 10}-272\cdot 25\right)$
$=\left(346.5-272.25\right)=74.25$.
$\therefore$ Variance, ${\sigma }^2=74.25$.