Question

The variance of first $10$multiples of $3$ is

• A. $64.25$
• B. $54.25$
• C. $70.25$
• D. $74.25$

Answer 1

The correct option is D $74.25$

${\sigma }^2=\frac{\sum _{i=1}^n{x}_i^2}{n}-{\overline{x}}^2$
The sample data is $3,6,\cdots ,30$
$\overline{x}=\frac{3(1+2+\cdots +10)}{10}=16.5$
$\sum _{i=1}^{10}{x}_i^2=\frac{9\left(10\right)(10+1)(2\times 10+1)}{6}=3465$
$\Rightarrow {\sigma }^2=\frac{3465}{10}-(16.5{)}^2=74.25$