Average of the squares of the first five naturals — Aptitude
Average of the squares of the first five naturals: What is the average of the squares of the first five natural… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the average of the squares of the first five natural numbers?
Options
- 9
- 11
- 13
- 15
Show the answer and the worked solution
Correct answer: B. 11
Worked solution
- Squares: 1 + 4 + 9 + 16 + 25 = 55.
- Average = 55 ÷ 5 = 11.
Answer: 11.
The idea
Squares are not evenly spaced, so the midpoint shortcut does not apply — add them. The formula n(n+1)(2n+1)/6 gives the sum directly if the list is long.
Shortcut. The average of the first n squares is (n + 1)(2n + 1)/6 = 6 × 11/6 = 11.
Common trap. "9" — squaring the middle number 3, as if the midpoint rule for evenly spaced lists applied to squares.