For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows the frequency distribution of the scores of the 9 players in group A and the 11 players in group B.
| Score | Group A | Group B |
|---|---|---|
| 2 | 1 | 0 |
| 3 | 1 | 0 |
| 4 | 2 | 0 |
| 5 | 1 | 4 |
| 6 | 3 | 2 |
| 7 | 0 | 0 |
| 8 | 0 | 2 |
| 9 | 1 | 1 |
| 10 | 0 | 2 |
| Total | 9 | 11 |
The median of the scores for group B is how much greater than the median of the scores for group A?
1. TRANSLATE the frequency table into actual data values
For Group A:
- The frequency table tells us:
- 1 player scored 2
- 1 player scored 3
- 2 players scored 4
- 1 player scored 5
- 3 players scored 6
- 1 player scored 9
- Total: 9 players
2. INFER that we need ordered lists to find medians
- Since median is the middle value, we need to list all scores in order
- Group A ordered scores: 2, 3, 4, 4, 5, 6, 6, 6, 9
3. TRANSLATE Group B's frequency table
For Group B:
- The frequency table tells us:
- 4 players scored 5
- 2 players scored 6
- 2 players scored 8
- 1 player scored 9
- 2 players scored 10
- Total: 11 players
4. Create ordered list for Group B
- Group B ordered scores: 5, 5, 5, 5, 6, 6, 8, 8, 9, 10, 10
5. INFER the median positions and SIMPLIFY to find values
- Group A has 9 values → median is the 5th value = \(\mathrm{5}\)
- Group B has 11 values → median is the 6th value = \(\mathrm{6}\)
6. SIMPLIFY to find the final difference
- Difference = \(\mathrm{6 - 5 = 1}\)
Answer: \(\mathrm{1}\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread the frequency table and think the frequencies ARE the actual scores, rather than understanding they represent how many players achieved each score.
For example, they might think Group A's data is: 1, 1, 2, 1, 3, 0, 0, 1, 0 instead of the actual scores: 2, 3, 4, 4, 5, 6, 6, 6, 9.
This fundamental misunderstanding makes it impossible to find the correct median and leads to confusion and guessing.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly understand the frequency table but make counting errors when determining which position represents the median, especially with larger datasets.
They might incorrectly identify the median position (like thinking the 4th position is the median for 9 values instead of the 5th position) and select the wrong middle value.
The Bottom Line:
The key challenge is recognizing that frequency tables compress repeated values - you must "expand" them back into complete ordered lists to properly locate the median position.