Question

the mean of the square of first 11 natural numbers is

Answer 1

1,2,3,4,5,6,7,8,9,10,11
mean=66/11
=6 is the answer of your question

Answer 2

The mean of the square of first 11 natural numbers is 46.

Step-by-step explanation:

The square of first 11 natural numbers are

$1^2,2^2,3^2,4^2,5^2,6^2,7^2,8^2,9^2,10^2,11^2$

To find, the mean of the square of first 11 natural numbers =?

We know that,

The sum of the square of first n natural numbers

$1^{2} +2^{2} +3^{2} +.....+n^2$

$=\dfrac{1}{6} n(n+1)(2n+1)$

∴ The sum of the square of first 11 natural numbers

Put n = 11

$=\dfrac{1}{6} \times 11(11+1)(2(11)+1)$

$=\dfrac{1}{6} \times 11(12)(23)$

$= 11\times 2\times 23$

∴ The mean of the square of first 11 natural numbers =$\dfrac{11\times 2\times 23}{11}$

$=2\times 23=46$

Thus, the mean of the square of first 11 natural numbers is 46.