Question

Let $x_1,x_2,....,x_n$ be n observations such that $\sum x_1^2=400$ and $\sum x_1=80$. Then the possible value of n among the following is

• A. 18
• B. 15
• C. 12
• D. 9

Answer 1

Answer: (A)

18

Using well known fact that root mean square of numbers $\ge$ A.M. of the numbers
$\Rightarrow \sqrt{\frac{400}{n}}\ge \frac{80}{n}\Rightarrow \frac{20}{\sqrt{n}}\ge \frac{80}{n}\Rightarrow \sqrt{n}\ge 4\Rightarrow n\ge 16$
$\Rightarrow$ Hence option A is correct choice.