A survey recorded the number of books each of 9 students finished last month. A dot plot of the data...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A survey recorded the number of books each of 9 students finished last month. A dot plot of the data shows 4 dots above 2, 3 dots above 4, and 2 dots above 6. Which frequency table correctly represents the individual frequencies for this data?
- Number: 2, 4, 6; Frequency: 4, 3, 2
- Number: 2, 4, 6; Frequency: 3, 4, 2
- Number: 4, 3, 2; Frequency: 2, 4, 6
- Number: 2, 5, 6; Frequency: 4, 3, 2
- Number: 2, 4, 6; Frequency: 4, 7, 9
1. TRANSLATE the dot plot information
- Given information:
- 4 dots above 2 → 4 students finished 2 books
- 3 dots above 4 → 3 students finished 4 books
- 2 dots above 6 → 2 students finished 6 books
2. INFER what the frequency table should contain
- A frequency table for individual frequencies shows:
- Number column: The different values that occurred (2, 4, 6 books)
- Frequency column: How many students had each value (4, 3, 2 students)
3. TRANSLATE this into proper frequency table format
- Number: 2, 4, 6
- Frequency: 4, 3, 2
4. Compare with answer choices
- Choice (A): Number: 2, 4, 6; Frequency: 4, 3, 2 ✓
- All other choices have errors in numbers, frequencies, or organization
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misread or misinterpret what "dots above" means in the dot plot description. They might think "4 dots above 2" means the number 4 appears above the number 2, rather than understanding this means 4 students (represented by 4 dots) read 2 books.
This leads to confusion about which numbers go in which column, potentially causing them to select Choice (C) (Number: 4, 3, 2; Frequency: 2, 4, 6) where the numbers and frequencies are completely reversed.
Second Most Common Error:
Poor TRANSLATE reasoning: Students correctly understand the dot plot but confuse individual frequencies with cumulative frequencies. They might calculate running totals: 4 students read 2 books, \(4+3=7\) students read 4 books or fewer, \(4+3+2=9\) students total.
This may lead them to select Choice (E) (Number: 2, 4, 6; Frequency: 4, 7, 9) thinking these cumulative counts are what the frequency table should show.
The Bottom Line:
Success requires careful reading of the dot plot description and clear understanding that "individual frequencies" means counting how many students achieved each specific number of books, not running totals or other arrangements.