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 will the mean and median of the scores change?
- AMean increases, Median stays the same
- BMean increases, Median decreases
- CMean decreases, Median stays the same
- DMean decreases, Median decreases
Show answer & explanationAnswer & explanation
Correct answer: D. Mean decreases, Median decreases
Original scores: 75, 80, 85, 90, 95. Original Mean = (75+80+85+90+95) / 5 = 425 / 5 = 85. Original Median (middle value of sorted list) = 85. New scores: 60, 75, 80, 85, 90, 95. New Mean = (60+75+80+85+90+95) / 6 = 485 / 6 ≈ 80.83. New Median (average of the two middle values in sorted list of 6) = (80 + 85) / 2 = 82.5. Comparing: Mean changed from 85 to 80.83 (decreased). Median changed from 85 to 82.5 (decreased).
Why the other options are wrong
- A. Both statements are incorrect.
- B. The mean will decrease, not increase, because the new score is lower than the original mean.
- C. The median will decrease because the new score pulls the middle values down.
Impact of Outliers on Mean and Median
The mean is highly sensitive to extreme values (outliers), while the median is more resistant to their influence, changing less dramatically or not at all depending on the outlier's position relative to the middle values.
- Mean: Average of all values; affected by every value.
- Median: Middle value when data is ordered; less affected by extreme values.
- Adding a value below the original mean will decrease the mean.
- Adding a value below the original median will decrease the median (if the count changes to even or odd).
Memory trick: Mean is a magnet for extremes, Median is a steady middle ground.