Question

What is the arithmetic mean of the squares of first five natural numbers?

• A. $9$
• B. $11$
• C. $13$
• D. $15$

Answer 1

The correct option is B $11$

First five natural numbers are $1,2,3,4,5$.

We know, Mean is given by,

$\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$ $⟹\overline{x}=\frac{\sum x}{n}$.

Here, number of observations $=5$.

Given, to find the squares of first five natural numbers.

$\Rightarrow A.M=\frac{(1{)}^2+(2{)}^2+(3{)}^2+(4{)}^2+(5{)}^2}{5}$

$\Rightarrow A.M=\frac{1+4+9+16+25}{5}$

$\Rightarrow A.M=\frac{55}{5}=11$.

Therefore, option $B$ i correct.