The results of two independent surveys are shown in the table below.Men's HeightGroupSample sizeMean (centimeters)Standard deviation (centimeters)A2,5...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The results of two independent surveys are shown in the table below.
Men's Height| Group | Sample size | Mean (centimeters) | Standard deviation (centimeters) |
|---|---|---|---|
| A | 2,500 | 186 | 12.5 |
| B | 2,500 | 186 | 19.1 |
Which statement is true based on the table?
The Group A data set was identical to the Group B data set.
Group B contained the tallest participant.
The heights of the men in Group B had a larger spread than the heights of the men in Group A.
The median height of Group B is larger than the median height of Group A.
1. TRANSLATE the problem information
- Given information from the table:
- Group A: 2,500 men, mean height = 186 cm, standard deviation = 12.5 cm
- Group B: 2,500 men, mean height = 186 cm, standard deviation = 19.1 cm
- We need to determine which statement about these groups is true.
2. INFER what each statistical measure tells us
- Mean = average height (both groups have the same average)
- Standard deviation = measure of spread/variability (how much individual heights vary from the mean)
- Larger standard deviation = more spread out data
- Identical datasets must have identical means AND standard deviations
3. INFER by systematically checking each answer choice
Choice A: "The Group A data set was identical to the Group B data set"
- For datasets to be identical, all statistical measures must match
- Means are equal: \(186 = 186\) ✓
- Standard deviations are different: \(12.5 ≠ 19.1\) ✗
- Therefore, datasets are NOT identical
Choice B: "Group B contained the tallest participant"
- Standard deviation tells us about spread, not maximum/minimum values
- We cannot determine which group had the tallest person from this information
Choice C: "The heights of the men in Group B had a larger spread than the heights of the men in Group A"
- Standard deviation measures spread
- Group B standard deviation \(19.1 \gt 12.5\) (Group A standard deviation)
- Therefore, Group B has larger spread ✓
Choice D: "The median height of Group B is larger than the median height of Group A"
- We only know means, not medians
- Equal means don't guarantee equal (or unequal) medians
- Cannot determine median comparison from given information
Answer: C
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Not understanding what standard deviation represents or what information can be determined from limited statistical measures.
Students might think that a larger standard deviation automatically means larger values overall, leading them to incorrectly select Choice B or Choice D. Or they might not realize that identical datasets require matching standard deviations, potentially selecting Choice A because the means are equal.
The Bottom Line:
This problem requires understanding that different statistical measures tell us different things about data - means show central tendency while standard deviations show variability. Success depends on recognizing what conclusions can and cannot be drawn from limited statistical information.
The Group A data set was identical to the Group B data set.
Group B contained the tallest participant.
The heights of the men in Group B had a larger spread than the heights of the men in Group A.
The median height of Group B is larger than the median height of Group A.