The daily low temperatures for seven consecutive days were -{10, -4, -4, 2, 7, 12, 19} degrees Celsius. What is...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The daily low temperatures for seven consecutive days were \(-10, -4, -4, 2, 7, 12, 19\) degrees Celsius. What is the range of these temperatures?
1. TRANSLATE the problem information
- Given information: Daily low temperatures for seven days: -10, -4, -4, 2, 7, 12, 19 degrees Celsius
- What we need to find: The range of these temperatures
- What this means mathematically: \(\mathrm{Range = Maximum\;value - Minimum\;value}\)
2. INFER the approach
- To find the range, we need to identify the highest and lowest temperatures first
- Then subtract the lowest from the highest
3. Identify the maximum and minimum values
- Looking through the data: -10, -4, -4, 2, 7, 12, 19
- Maximum temperature: 19°C (the largest value)
- Minimum temperature: -10°C (the smallest value, remembering that -10 is smaller than -4)
4. SIMPLIFY the range calculation
- Range = Maximum - Minimum
- \(\mathrm{Range = 19 - (-10)}\)
- \(\mathrm{Range = 19 + 10 = 29}\)
Answer: 29
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak SIMPLIFY skill: Students make arithmetic errors when subtracting the negative minimum value.
They correctly identify max = 19 and min = -10, but then compute \(\mathrm{19 - (-10)}\) as \(\mathrm{19 - 10 = 9}\) instead of \(\mathrm{19 + 10 = 29}\). This happens because they forget that subtracting a negative number is the same as adding the positive number.
This leads to the wrong answer of 9.
Second Most Common Error:
Poor INFER reasoning: Students incorrectly think range means the difference between consecutive values or confuse range with other statistical measures.
Instead of finding max - min for the entire dataset, they might subtract consecutive temperatures (like \(\mathrm{19 - 12 = 7}\)) or try to find an average difference. This leads to confusion and various incorrect answers.
The Bottom Line:
This problem tests whether students truly understand what "range" means in statistics and can handle negative number arithmetic correctly. The combination of a simple concept with potentially tricky arithmetic makes it easy to get wrong despite seeming straightforward.