The list gives the mass, in grams, of 5 alpine marmots. 4{,010}; 4{,010}; 3{,030}; 4{,050}; 3{,050} What is the mean...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The list gives the mass, in grams, of \(\mathrm{5}\) alpine marmots.
\(\mathrm{4{,}010}\); \(\mathrm{4{,}010}\); \(\mathrm{3{,}030}\); \(\mathrm{4{,}050}\); \(\mathrm{3{,}050}\)
What is the mean mass, in grams, of these \(\mathrm{5}\) alpine marmots?
1. TRANSLATE the problem information
- Given information:
- 5 alpine marmot masses (in grams): 4,010; 4,010; 3,030; 4,050; 3,050
- Need to find the mean mass
- What this tells us: We need to calculate the average of these 5 numbers
2. SIMPLIFY by finding the sum
- Add all five masses together:
\(4{,}010 + 4{,}010 = 8{,}020\)
\(8{,}020 + 3{,}030 = 11{,}050\)
\(11{,}050 + 4{,}050 = 15{,}100\)
\(15{,}100 + 3{,}050 = 18{,}150\)
- Total sum = 18,150 grams
3. SIMPLIFY by calculating the mean
- Divide the sum by the number of values:
\(\mathrm{Mean} = 18{,}150 \div 5 = 3{,}630\) grams
Answer: 3,630
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak SIMPLIFY skill: Students make arithmetic errors when adding the five large numbers together.
Common mistakes include:
- Incorrectly carrying digits when adding (getting 17,150 instead of 18,150)
- Misaligning place values
- Adding carelessly and getting sums like 18,050 or 18,250
This leads to wrong final answers even though they understand the mean concept correctly.
Second Most Common Error:
Missing conceptual knowledge: Some students confuse mean with other measures like median or range.
They might arrange the numbers in order (3,030; 3,050; 4,010; 4,010; 4,050) and select the middle value (4,010) thinking this is the mean, when it's actually the median.
The Bottom Line:
This problem tests whether students can accurately perform multi-step arithmetic with larger numbers while applying the mean formula correctly. The concept is straightforward, but execution requires careful calculation.