Each value in the data set shown represents the height, in centimeters, of a plant.6, 10, 13, 2, 15, 22,...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Each value in the data set shown represents the height, in centimeters, of a plant.
6, 10, 13, 2, 15, 22, 10, 4, 4, 4
What is the mean height, in centimeters, of these plants?
1. TRANSLATE the problem requirements
- Given information:
- Data set with 10 plant heights: 6, 10, 13, 2, 15, 22, 10, 4, 4, 4
- Question asks for the mean height
- What this tells us: We need to calculate the arithmetic average of these values
2. SIMPLIFY by performing the mean calculation
- Add all the values together:
\(6 + 10 + 13 + 2 + 15 + 22 + 10 + 4 + 4 + 4 = 90\)
- Count the number of data points: 10 plants
- Apply the mean formula:
\(\mathrm{Mean} = \frac{\mathrm{Sum}}{\mathrm{Number\,of\,values}}\)
\(\mathrm{Mean} = \frac{90}{10} = 9\)
Answer: 9
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak SIMPLIFY execution: Making arithmetic errors when adding the ten values
Students may miscount repeated values (three 4's, two 10's) or make simple addition mistakes, getting sums like 86 or 94 instead of 90. This leads to incorrect final answers like 8.6 or 9.4, causing them to get stuck and guess from available choices.
Second Most Common Error:
Poor TRANSLATE reasoning: Confusing mean with other measures of central tendency
Some students might calculate the median instead of the mean, arranging values in order (2, 4, 4, 4, 6, 10, 10, 13, 15, 22) and finding the middle values (6 and 10), leading them to report 8 as the answer.
The Bottom Line:
This problem tests careful arithmetic execution more than conceptual complexity. Success requires systematic addition of all values and accurate division, making computational accuracy the primary challenge.