The table below shows the distribution of points scored by a basketball player in 19 different games.Points ScoredFrequency (Number of...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The table below shows the distribution of points scored by a basketball player in 19 different games.
| Points Scored | Frequency (Number of Games) |
|---|---|
| 5 | 8 |
| 10 | 3 |
| 15 | 4 |
| 20 | 2 |
| 25 | 2 |
What is the median number of points the player scored?
5
10
12
15
1. TRANSLATE the problem information
- Given information:
- Frequency table showing points scored across 19 games
- Need to find the median (middle value)
- What this tells us: We need to find the middle score when all 19 games are arranged in order from lowest to highest
2. INFER the approach
- Since we have 19 games (odd number), the median will be the single middle value
- The median position is \(\mathrm{n} + 1)/2 = (19 + 1)/2 = 10\)th game
- Since data is grouped by frequency, we need cumulative frequency to locate the 10th game
3. SIMPLIFY by building cumulative frequency
- Games 1-8: all scored 5 points
- Games 9-11: all scored 10 points (running total: \(8 + 3 = 11\) games)
- Games 12-15: all scored 15 points (running total: \(11 + 4 = 15\) games)
- Games 16-17: all scored 20 points (running total: \(15 + 2 = 17\) games)
- Games 18-19: all scored 25 points (running total: \(17 + 2 = 19\) games)
4. INFER the final answer
- The 10th game falls within games 9-11 (which all scored 10 points)
- Therefore, the median is 10 points
Answer: B (10)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students often confuse median with mode or try to calculate an average of the score values rather than finding the actual middle position.
They might think: "The most frequent score is 5 points (8 games), so that must be the median" or "Let me average all the different point values: \((5 + 10 + 15 + 20 + 25)/5 = 15\)."
This may lead them to select Choice A (5) for mode confusion or Choice D (15) for the averaging error.
Second Most Common Error:
Poor TRANSLATE reasoning: Students misunderstand what the 10th position means and incorrectly think the median should be between two values, leading them to calculate \((5 + 15)/2 = 10\) or \((10 + 15)/2 = 12.5 ≈ 12\).
This may lead them to select Choice C (12) thinking they need to average adjacent groups.
The Bottom Line:
This problem requires students to understand that finding a median from a frequency table means locating the actual middle data point using cumulative frequency, not performing calculations on the score categories themselves.
5
10
12
15