Question

The average of the squares of the first ten natural number is:

• A. $40$
• B. $50$
• C. $47.5$
• D. $38.5$

Answer 1

The correct option is D $38.5$

Average is the sum of the data values divided by the total number of data values.

Squares of the first ten natural numbers are $1^2,2^2,3^2,4^2,5^2,6^2,7^2,8^2,9^2,{10}^2$

Therefore, average $=\frac{1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2+{10}^2}{10}$

$=\frac{1+4+9+16+25+36+49+64+81+100}{10}$

$=\frac{385}{10}=38.5$