Three sections of a year group — Averages Aptitude Question
Three sections of a year group: Three classes have 25, 30 and 45 students with average marks 50, 60 and 70… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Three classes have 25, 30 and 45 students with average marks 50, 60 and 70 respectively. What is the overall average?
Options
- 60
- 62
- 64
- 65
Show the answer and the worked solution
Correct answer: B. 62
Worked solution
- Totals: 25 × 50 = 1,250; 30 × 60 = 1,800; 45 × 70 = 3,150.
- Sum = 6,200 over 100 students.
- Average = 62.
Answer: 62.
The idea
Weighted average across any number of groups: sum of (count × average) divided by the total count. The plain mean of 50, 60 and 70 is 60 and is wrong.
Shortcut. Measure from 60: 25 students at −10 and 45 at +10 net +200 over 100 students, so 60 + 2 = 62.
Common trap. "60" — the plain mean of 50, 60 and 70; the biggest class scores 70, so the overall average must sit above 60.