Descriptive Statistics
Two distinct groups contain twenty and thirty students with mean marks of sixty and seventy respectively in an examination; find the combined mean mark of all fifty students taken together.
Select the correct option:
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About This Question
- Subject
- mathematics
- Chapter
- statistics and probability
- Topic
- descriptive statistics
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
66
The combined mean of several groups is the total of all observations divided by the total count, equivalently a weighted average of group means with weights equal to group sizes. This grouped-mean computation appears regularly in JEE Advanced statistics. The first group contributes 20 × 60 = 1200 total marks and the second contributes 30 × 70 = 2100 total marks, giving a grand total of 1200 + 2100 = 3300 across 20 + 30 = 50 students. Hence the combined mean is 3300/50 = 66. Option 65 results from naively averaging 60 and 70 while ignoring the unequal group sizes. Option 64 under-weights the larger second group. Option 68 over-weights it. The principle is the weighted mean x̄ = (n₁x̄₁ + n₂x̄₂)/(n₁ + n₂), reflecting that larger groups influence the overall average more. Plausibility check: 66 lies between the two group means 60 and 70 and is pulled toward 70 because the larger group of 30 students has the higher mean, which matches the weighting intuition.
This easy difficulty mathematics question is from the chapter statistics and probability, covering the topic of descriptive statistics. It appeared in the 2025 exam.
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