Question : What is the average of the squares of the first five natural numbers?
Option 1: 11.5
Option 2: 10
Option 3: 12.5
Option 4: 11
Correct Answer: 11
Solution :
The sum of the square of first $n$ natural numbers = $\frac{n(n+1)(2n+1)}{6}$, where $n$ is the number of numbers.
Here, $n = 5$
⇒ Sum = $\frac{5(5+1)(10+1)}{6}=\frac{5(6)(11)}{6}=55$
$\therefore$ Average $=\frac{55}{5}=11$
Hence, the correct answer is 11.
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