Question

What is the mean of the squares of the first 20 natural numbers ?

• A. $15.5$
• B. $143.5$
• C. $65$
• D. $72$

Answer 1

Answer: (B)

$143.5$

The formula for sum of square of first n natural numbers is given by

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

Mean of a set of $n$ numbers

$=\frac{\text{sum of numbers}}{n}=\frac{\frac{n(n+1)(2n+1)}{6}}{n}=\frac{(n+1)(2n+1)}{6}\because n=20$

$\therefore Mean=143.5$