Question
Reese's test scores were 93, 93, 85, 89, and 90. She forgot to study and made 48 on the next test. Which THREE statements are correct?
Responses
A The mean is the best measure to describe the data.The mean is the best measure to describe the data.
B The outlier, 48, lowers Reese's average by 7 points.The outlier, 48, lowers Reese's average by 7 points.
C The median is the best measure to describe the data.The median is the best measure to describe the data.
D The median changes from 90 to 89.5 after the last test.The median changes from 90 to 89.5 after the last test.
E The last test score had the greatest effect on the median.
Responses
A The mean is the best measure to describe the data.The mean is the best measure to describe the data.
B The outlier, 48, lowers Reese's average by 7 points.The outlier, 48, lowers Reese's average by 7 points.
C The median is the best measure to describe the data.The median is the best measure to describe the data.
D The median changes from 90 to 89.5 after the last test.The median changes from 90 to 89.5 after the last test.
E The last test score had the greatest effect on the median.
Answers
GPT-4o mini
To analyze Reese's test scores and determine which statements are correct, let's first calculate the mean and median of the initial set of scores and then include the outlier score (48):
Initial scores: 93, 93, 85, 89, 90
1. **Calculate the mean of the initial scores:**
- Mean = (93 + 93 + 85 + 89 + 90) / 5
- Mean = 450 / 5 = 90
2. **Calculate the mean including the outlier:**
- New scores: 93, 93, 85, 89, 90, 48
- New mean = (93 + 93 + 85 + 89 + 90 + 48) / 6
- New mean = 498 / 6 = 83
3. **Calculate the median of the initial scores:**
- Ordered scores: 85, 89, 90, 93, 93
- Median (middle value) = 90
4. **Calculate the median including the outlier:**
- Ordered new scores: 48, 85, 89, 90, 93, 93
- New median = (89 + 90) / 2 = 89.5 (the average of the two middle values, since there are now an even number of scores)
Now, let's evaluate each statement based on this information:
A. **The mean is the best measure to describe the data.**
- False. The mean is heavily affected by the outlier (48), so it is not the best measure.
B. **The outlier, 48, lowers Reese's average by 7 points.**
- True. The mean dropped from 90 to 83, which is a decrease of 7 points.
C. **The median is the best measure to describe the data.**
- True. The median is less affected by the outlier and provides a better representation of the middle of the data.
D. **The median changes from 90 to 89.5 after the last test.**
- True. The median changed from 90 to 89.5.
E. **The last test score had the greatest effect on the median.**
- False. The last test score did affect the median, but it is not the greatest effect; it was already shifted by introducing an extremely low score.
Thus, the correct three statements are B, C, and D.
Initial scores: 93, 93, 85, 89, 90
1. **Calculate the mean of the initial scores:**
- Mean = (93 + 93 + 85 + 89 + 90) / 5
- Mean = 450 / 5 = 90
2. **Calculate the mean including the outlier:**
- New scores: 93, 93, 85, 89, 90, 48
- New mean = (93 + 93 + 85 + 89 + 90 + 48) / 6
- New mean = 498 / 6 = 83
3. **Calculate the median of the initial scores:**
- Ordered scores: 85, 89, 90, 93, 93
- Median (middle value) = 90
4. **Calculate the median including the outlier:**
- Ordered new scores: 48, 85, 89, 90, 93, 93
- New median = (89 + 90) / 2 = 89.5 (the average of the two middle values, since there are now an even number of scores)
Now, let's evaluate each statement based on this information:
A. **The mean is the best measure to describe the data.**
- False. The mean is heavily affected by the outlier (48), so it is not the best measure.
B. **The outlier, 48, lowers Reese's average by 7 points.**
- True. The mean dropped from 90 to 83, which is a decrease of 7 points.
C. **The median is the best measure to describe the data.**
- True. The median is less affected by the outlier and provides a better representation of the middle of the data.
D. **The median changes from 90 to 89.5 after the last test.**
- True. The median changed from 90 to 89.5.
E. **The last test score had the greatest effect on the median.**
- False. The last test score did affect the median, but it is not the greatest effect; it was already shifted by introducing an extremely low score.
Thus, the correct three statements are B, C, and D.