The average of the squares of the first 45 natural numbers is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 697.67.
We know that,
The sum of squares = n(n + 1)(2n + 1)/6
here, n = number of terms = 45
The sum of squares = 45(45 + 1)(2 × 45 + 1)/6
⇒ (45 × 46 × 91)/6
⇒ 188370/6 = 31395
Now,
Average = Sum of observations/Number of observations
Average = 31395/45 = 697.67