2017 · Q100
The average height of 22 students of a class is 140 cm and the average height of 28 students of another class is 152 cm. What is the average height of students of both the classes ?
Elementary MathematicsStatistics
- A144.32 cm
- B145.52 cm
- C146.72 cm
- D147.92 cm
Explanation
A combined average is a weighted mean, weighted by class sizes: (22 × 140 + 28 × 152)/(22 + 28). The total heights are 3080 cm and 4256 cm, summing to 7336 cm over 50 students. This gives 7336/50 = 146.72 cm. The unweighted mean of 140 and 152 (146 cm) is wrong because the classes are unequal in size — the larger class pulls the average toward 152. Hence option (C) 146.72 cm.