Question

If $x_1,x_2,...,x_n$ be $n$ observations such that $\sum _{i=1}^n{x}_i^2=400$ and $\sum _{i=1}^n{x}_1=80$. Then, a possible value of $n$ among the following is

• A. $9$
• B. $12$
• C. $15$
• D. $18$

Answer 1

Answer: (D)

$18$

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