Question
The points scored per game by a professional basketball player are represented by the box plot below.
A number line plots points per game by the basketball player. The plots are 16 through 21 and 21 through 24.
If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected?
A.
The median points per game decreases.
B.
The effect on the median points per game cannot be determined.
C.
The median points per game is not affected.
D.
The median points per game increases.
A number line plots points per game by the basketball player. The plots are 16 through 21 and 21 through 24.
If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected?
A.
The median points per game decreases.
B.
The effect on the median points per game cannot be determined.
C.
The median points per game is not affected.
D.
The median points per game increases.
Answers
GPT-4o mini
To determine how the median is affected by adding the two new scores (9 and 35), we first need to understand the original distribution represented by the box plot, which shows points ranging from 16 through 21 and 21 through 24.
Here are the steps to analyze the situation:
1. **Understand the Original Distribution**: The box plot generally represents a dataset of scores. We know that scores range from around 16 to 24. Without specific details on the exact data points, we can guess that the middle score (the median) lies somewhere between 21 and the upper range around 24.
2. **Add the New Scores**: We are adding two new scores: 9 and 35.
3. **Ordering the Scores**:
- The original scores are likely centered between 16 and 24.
- When we add 9 (which is quite low) and 35 (which is quite high), these two extreme values will likely affect the median.
4. **Determine Median Position**:
- The median is the middle score when the numbers are ordered.
- Adding the new scores of 9 and 35 will widen the distribution significantly: The new set will now include lower (9) and higher (35) extremes than the original scores.
5. **Conclusion about the Median**:
- With 9, the lower half will effectively shift, and the previous middle scores will likely move down as there are now more lower scores, pulling the median down.
- The score of 35 does not shift the median up since it is much higher than the existing scores and affects more of the higher end than the lower end.
- Thus, the new median, when recalculated with the new scores, would be lower than the previous median.
The correct answer is:
**A. The median points per game decreases.**
Here are the steps to analyze the situation:
1. **Understand the Original Distribution**: The box plot generally represents a dataset of scores. We know that scores range from around 16 to 24. Without specific details on the exact data points, we can guess that the middle score (the median) lies somewhere between 21 and the upper range around 24.
2. **Add the New Scores**: We are adding two new scores: 9 and 35.
3. **Ordering the Scores**:
- The original scores are likely centered between 16 and 24.
- When we add 9 (which is quite low) and 35 (which is quite high), these two extreme values will likely affect the median.
4. **Determine Median Position**:
- The median is the middle score when the numbers are ordered.
- Adding the new scores of 9 and 35 will widen the distribution significantly: The new set will now include lower (9) and higher (35) extremes than the original scores.
5. **Conclusion about the Median**:
- With 9, the lower half will effectively shift, and the previous middle scores will likely move down as there are now more lower scores, pulling the median down.
- The score of 35 does not shift the median up since it is much higher than the existing scores and affects more of the higher end than the lower end.
- Thus, the new median, when recalculated with the new scores, would be lower than the previous median.
The correct answer is:
**A. The median points per game decreases.**