Question

If the mean of $n$ observations $1^2, 2^2, 3^2, \ldots, n^2$ is $\frac{46 n}{11}$, then $n$ is equal to

(a) 11

(b) 12

(c) 23

(d) 22

Answer 1

Mean of $1^2, 2^2, 3^2, \ldots, n^2$ is $\frac{\Sigma n^2}{n}$

$\begin{array}{ll}\therefore & \frac{n(n+1)(2 n+1)}{6 n}=\frac{46 n}{11} \\\Rightarrow & (n-11)(22 n-1)=0 \\\Rightarrow & n=11 \text { as } n \neq \frac{1}{22}\end{array}$

So, The correct option of this question will be (A).