The high temperature, in degrees Fahrenheit (^circF), in a certain city was recorded for each of 5 days. The data...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The high temperature, in degrees Fahrenheit (\(^\circ\mathrm{F}\)), in a certain city was recorded for each of 5 days. The data are shown below.
| Day | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| High temperature (\(^\circ\mathrm{F}\)) | \(81\) | \(80\) | \(81\) | \(81\) | \(82\) |
Over this 5-day period, which of the following is NOT equal to \(81^\circ\mathrm{F}\)?
Median of the high temperatures
Mean of the high temperatures
Mode of the high temperatures
Range of the high temperatures
1. TRANSLATE the problem information
- Given information:
- Temperature data for 5 days: 81, 80, 81, 81, 82 (°F)
- Need to find median, mean, mode, and range
- Question asks which is NOT equal to 81°F
2. INFER the systematic approach
- Calculate all four statistical measures first
- Compare each result to 81°F to find the exception
- Remember: we need the one that's different from 81°F
3. Calculate the median
- VISUALIZE by ordering the data: 80, 81, 81, 81, 82
- With 5 values, median is the 3rd value = 81°F
4. SIMPLIFY to find the mean
- Sum: \(\mathrm{81 + 80 + 81 + 81 + 82 = 405}\)
- Mean = \(\mathrm{405 \div 5 = 81°F}\)
5. Find the mode
- INFER which value appears most frequently
- 80 appears 1 time, 81 appears 3 times, 82 appears 1 time
- Mode = 81°F
6. Calculate the range
- Range = Maximum - Minimum = \(\mathrm{82 - 80 = 2°F}\)
7. INFER the final answer
- Median = 81°F ✓
- Mean = 81°F ✓
- Mode = 81°F ✓
- Range = 2°F ← This is NOT equal to 81°F
Answer: D. Range of the high temperatures
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may misread the question and look for what IS equal to 81°F instead of what is NOT equal to 81°F.
After correctly calculating all measures, they see that median, mean, and mode all equal 81°F and incorrectly think this makes all of them correct answers. They might select Choice A, B, or C without carefully reading that the question asks for the exception.
Second Most Common Error:
Missing conceptual knowledge of range: Students may confuse range with one of the other statistical measures or calculate it incorrectly.
Some might think range means the "most common range of values" and incorrectly identify 81°F as the range since it appears most frequently. This conceptual confusion leads them to select Choice A, B, or C when they should recognize that range = 2°F.
The Bottom Line:
This problem tests both statistical knowledge and careful reading comprehension. Success requires knowing all four statistical definitions AND paying close attention to the word "NOT" in the question stem.
Median of the high temperatures
Mean of the high temperatures
Mode of the high temperatures
Range of the high temperatures