Find the average of squares of first five natural numbers.

The correct answer is Option (3) → 11

The average is the sum of the values divided by their number; here the values are the squares of 1, 2, 3, 4 and 5.

• Sum \(=1+4+9+16+25=55\)

• Average \(=\displaystyle\frac{55}{5}=11\)

Tip: The sum of the squares of the first \(n\) natural numbers is \(\displaystyle\frac{n(n+1)(2n+1)}{6}\), so their average is \(\displaystyle\frac{(n+1)(2n+1)}{6}\); for \(n=5\) it is \(\displaystyle\frac{6\times11}{6}=11\).