The histogram summarizes the distribution of an original data set that represents the number of points per game a basketball team has scored in the last 50 games played. If the team scores 18 points in the next game and this game is added to the original data set to create a new data set of 51 values, which of the following must be true?
I. The median number of points per game for the new data set is less than the median number of points per game for the original data set.
II. The mean number of points per game for the new data set is less than the mean number of points per game for the original data set.
Explanation
Context: Histogram of 50 basketball game scores, mostly 50–60. Team scores 18 points in next game (added to create 51 values).
Answer: B) II only
Why:
- Statement I (Median): With 50 values, median = avg of 25th & 26th (both in 50–60). With 51 values after adding 18 at the bottom, new median = 26th = old 25th, still in 50–60. Median doesn't decrease. ✗
- Statement II (Mean): 18 is well below the mean (~50–55). Adding a value below the mean always decreases it. ✓
Traps: A ("I only") is wrong because the median doesn't change. C ("I and II") incorrectly assumes both change.