Question
The distribution of golf scores for a class are represented by the dot plot below.
A golf score of 84 was later added to the data set.
Which of the following is not true about the data set when the new score is included?
(1 point)
Responses
The interquartile range of the scores decreases.
The interquartile range of the scores decreases.
The standard deviation of the scores increases.
The standard deviation of the scores increases.
The mean score increases.
The mean score increases.
The median score stays the same.
The median score stays the same.
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A golf score of 84 was later added to the data set.
Which of the following is not true about the data set when the new score is included?
(1 point)
Responses
The interquartile range of the scores decreases.
The interquartile range of the scores decreases.
The standard deviation of the scores increases.
The standard deviation of the scores increases.
The mean score increases.
The mean score increases.
The median score stays the same.
The median score stays the same.
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Answers
GPT-4o mini
To evaluate which statement is not true after adding the golf score of 84 to the data set, let's analyze each option:
1. **The interquartile range of the scores decreases.**
- The interquartile range (IQR) measures the middle 50% of the data (the difference between the first quartile \( Q1 \) and the third quartile \( Q3 \)). Adding a score of 84 may change the quartiles, but it generally does not decrease the range of scores. If 84 is outside or on the boundaries of the current IQR, it likely won't decrease the IQR.
2. **The standard deviation of the scores increases.**
- Standard deviation measures the spread of the data. If the new score of 84 is outside the mean of the existing scores, this can increase the standard deviation since the overall variability would increase. Therefore, this statement is likely true.
3. **The mean score increases.**
- Adding a score of 84 to the data set will generally increase the mean if 84 is higher than the current mean of the scores, which seems likely in the context of golf scores. However, if the existing mean is already high or 84 is low relative to the mean, the mean may not change or could even decrease, making this statement potentially untrue depending on the context.
4. **The median score stays the same.**
- The median, which represents the middle value of a sorted data set, may or may not change depending on where 84 fits within the existing scores. If 84 does not change the position of the median, this statement may hold true; however, if the addition of 84 changes the order of scores significantly and moves the median position, then the median would change.
Given these evaluations, the statement that is most likely not true is:
**The interquartile range of the scores decreases.**
This is because adding a score to a data set typically does not lead to a decrease in the spread measured by the IQR.
1. **The interquartile range of the scores decreases.**
- The interquartile range (IQR) measures the middle 50% of the data (the difference between the first quartile \( Q1 \) and the third quartile \( Q3 \)). Adding a score of 84 may change the quartiles, but it generally does not decrease the range of scores. If 84 is outside or on the boundaries of the current IQR, it likely won't decrease the IQR.
2. **The standard deviation of the scores increases.**
- Standard deviation measures the spread of the data. If the new score of 84 is outside the mean of the existing scores, this can increase the standard deviation since the overall variability would increase. Therefore, this statement is likely true.
3. **The mean score increases.**
- Adding a score of 84 to the data set will generally increase the mean if 84 is higher than the current mean of the scores, which seems likely in the context of golf scores. However, if the existing mean is already high or 84 is low relative to the mean, the mean may not change or could even decrease, making this statement potentially untrue depending on the context.
4. **The median score stays the same.**
- The median, which represents the middle value of a sorted data set, may or may not change depending on where 84 fits within the existing scores. If 84 does not change the position of the median, this statement may hold true; however, if the addition of 84 changes the order of scores significantly and moves the median position, then the median would change.
Given these evaluations, the statement that is most likely not true is:
**The interquartile range of the scores decreases.**
This is because adding a score to a data set typically does not lead to a decrease in the spread measured by the IQR.