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. $12$
• D. $9$

Answer 1

The correct option is B $18$

We know that $\text{AM of}{n}^{th}\text{power}>n^{th}\text{power of AM}$

$\frac{\sum x_i^2}{n}\ge (\frac{\sum x_i}{n}{)}^2$

Given that $\sum x_i^2=400$ and $\sum x_i=80$

Therefore, $\frac{400}{n}>(\frac{80}{n}{)}^2$

$⟹\frac{400}{n}>\left(\frac{6400}{n^2}\right)$

$⟹400n>6400$

$⟹n>\frac{6400}{400}$

$⟹n>16$

Therefore, the possible value of $n$ from the given options is $18$