Question : What is the average of the squares of the first 19 natural numbers?
Option 1: 124
Option 2: 127.5
Option 3: 130
Option 4: 133.5
Correct Answer: 130
Solution :
Given: 19 natural numbers.
Sum of first n natural numbers = $\frac{\text{n(n+1)(2n+1)}}{6}$
Sum of first 19 natural numbers = $\frac{\text{19(19+1)(2×19+1)}}{6}$ = $\frac{\text{14820}}{6}$ = 2470
Average of these numbers = $\frac{\text{Sum of first 19 natural numbers}}{19}$ = $\frac{\text{2470}}{19}$ = 130
Hence, the correct answer is 130.
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