GRE General TestQuantitative ReasoningMedium
A data analyst is examining a set of exam scores: 75, 80, 85, 90, 95. If a new score of 60 is added to the set, how does the median of the scores change?
- AThe median decreases by 5.
- BThe median decreases by 2.5.
- CThe median remains the same.
- DThe median increases by 5.
Show answer & explanationAnswer & explanation
Correct answer: B. The median decreases by 2.5.
Original set: 75, 80, 85, 90, 95. Median is 85. New set: 60, 75, 80, 85, 90, 95. With an even number of data points, the median is the average of the two middle numbers (80+85)/2 = 82.5. Change = 85 - 82.5 = 2.5 decrease.
Why the other options are wrong
- A. This is incorrect; the decrease is 2.5, not 5.
- C. Adding a new value, especially an outlier, typically changes the median.
- D. The median decreases, it does not increase.
Median with Even/Odd Data Sets
The median is the middle value in an ordered dataset. For an odd number of data points, it's the single middle value. For an even number, it's the average of the two middle values.
- Always order data from least to greatest first.
- Odd count: (n+1)/2 position.
- Even count: average of n/2 and (n/2)+1 positions.
Memory trick: Middle number moves when the list grows.