Average of squares of of first ten natural numbers is

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The average of the squares of of first ten natural numbers is

A

$35.5$

B

$36$

C

$37.5$

D

$38.5$

Solution

The sum of the squares of $n$ Natural numbers

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

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

Average Square of $10$ Natural number

$=\frac{11 \times 21}{6}=\frac{77}{2}=38.5$

Standard 13

Quantitative Aptitude

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