Question 101

The average of 1^2 , 2^2 , 3^2 , 4^2 , 5^2 , 6^2 , 7^2 , 8^2 , 9^2 , 10^2 is :

Solution

sum of squares of first n natural numbers are $$\frac{(n)(n+1)(2n+1)}{6}$$

average = $$\frac{SumofElements}{NmberofElements}$$

we are given numbers as 1^2 , 2^2 , 3^2 , 4^2 , 5^2 , 6^2 , 7^2 , 8^2 , 9^2 , 10^2

Sum of 10 elements = $$\frac{10 \times 11 \times 21}{6}$$ = 385

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

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