Question

Find the mean of first four square numbers.

Answer 1

The first n natural numbers are 1,2,3,...,n

Sum of squares of n natural numbers is

$1 </p><p>2</p><p> +2 </p><p>2</p><p> +3 </p><p>2</p><p> +...+n </p><p>2$

We know that sum of squares of first n natural numbers is given by

n(n+1)(2n+1)/6

Mean is the average of the values of the data set.

Therefore, mean of the squares of first n natural numbers is

$n</p><p>1 </p><p>2</p><p> +2 </p><p>2</p><p> +3 </p><p>2</p><p> +...+n </p><p>2$

$n(n+1)(2n+1)</p><p> </p><p> = </p><p>6</p><p>(n+1)(2n+1)$