Question

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

• A. 9
• B. 12
• C. 15
• D. 18

Answer 1

The correct option is D 18

Since, root mean square $\ge$ arithmetic mean $\therefore \sqrt{\frac{\sum _{i=1}^n{x}_1^2}{n}}\ge \frac{\sum _{i=1}^n{x}_i}{n}=\sqrt{\frac{400}{n}}\ge \frac{80}{n}\Rightarrow n\ge 16$ Hence, possible value of $n=18$