Question

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

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

Answer 1

Answer: (B)

$18$

Variance $=E\left(X^2\right)-\left(E\right(X){)}^2$

$=\frac{\sum x_i^2}{n}-(\frac{\sum x}{n}{)}^2$

$=\frac{400}{n}-\frac{6400}{n^2}$

$=\frac{400n-6400}{n^2}$

Standard deviation $=\sqrt{Var}$

$=\sqrt{\frac{400n-6400}{n^2}}$

Therefore, $\frac{400n-6400}{n^2}\ge 0$

$400n-6400\ge 0$

$n\ge 16$.