Five sunflowers each have heights recorded. The table shows the original data set of the heights in centimeters.PlantHeight (cm)A185B172C190D168E177A ...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Five sunflowers each have heights recorded. The table shows the original data set of the heights in centimeters.
| Plant | Height (cm) |
|---|---|
| A | 185 |
| B | 172 |
| C | 190 |
| D | 168 |
| E | 177 |
A sixth plant with height 155 cm is added to create a new data set. Which of the following correctly compares the medians of the two data sets?
The median of the original data set is greater than the median of the new data set.
The median of the original data set is less than the median of the new data set.
The medians of both data sets are equal.
There is not enough information to compare the medians.
1. TRANSLATE the problem information
- Given information:
- Original data set: Plant heights of 185, 172, 190, 168, 177 cm
- New data set: Original data plus a sixth plant with height 155 cm
- Need to compare the medians of both data sets
- What this tells us: We need to find the median for a 5-value data set, then for a 6-value data set, then compare them.
2. INFER the approach needed
- Key insight: The median calculation method will be different for the two data sets
- Original set (5 values): Median = middle value
- New set (6 values): Median = average of two middle values
- Strategy: Find each median separately, then compare
3. SIMPLIFY the original data set median
- Order the original heights: 168, 172, 177, 185, 190
- With 5 values, the median is the 3rd value: 177 cm
4. SIMPLIFY the new data set median
- Order all six heights: 155, 168, 172, 177, 185, 190
- With 6 values, the median is the average of the 3rd and 4th values:
- Median = \((172 + 177) ÷ 2 = 349 ÷ 2 = 174.5\) cm
5. INFER the comparison result
- Original median: 177 cm
- New median: 174.5 cm
- Since \(177 \gt 174.5\), the original median is greater than the new median
Answer: A
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak SIMPLIFY execution: Students often fail to properly order the data before finding the median, or they forget to average the two middle values for even-numbered data sets.
For example, they might try to find the median of the original set without ordering it first, incorrectly identifying 190 as the median since it appears in the middle of the table. Or when working with the new 6-value set, they might just pick the 3rd or 4th value instead of averaging them, leading to medians like 172 or 177 instead of 174.5.
This leads to confusion about which median is actually larger and may result in guessing among the answer choices.
Second Most Common Error:
Poor TRANSLATE reasoning: Students may misunderstand what happens when a data point is added to a set, particularly not recognizing that the calculation method for median changes from odd to even number of values.
They might assume both medians should be calculated the same way, leading them to incorrectly find the median of the 6-value set as a single middle value rather than an average.
This may lead them to select Choice B or C if their calculation errors happen to make the new median appear larger or equal to the original.
The Bottom Line:
This problem tests whether students truly understand that median calculation depends on whether you have an odd or even number of data points, and requires careful attention to ordering and arithmetic accuracy.
The median of the original data set is greater than the median of the new data set.
The median of the original data set is less than the median of the new data set.
The medians of both data sets are equal.
There is not enough information to compare the medians.