Question
The distribution of golf scores for a class are represented by the dot plot below.
74 has 0 dots
between has 1
76 has 0
between has 2
78 has 3
between has 2
80 has 2
between has 1
and 82 through 84 has 0
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 mean score increases.
The mean score increases.
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 median score stays the same.
74 has 0 dots
between has 1
76 has 0
between has 2
78 has 3
between has 2
80 has 2
between has 1
and 82 through 84 has 0
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 mean score increases.
The mean score increases.
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 median score stays the same.
Answers
GPT-4o mini
To evaluate which statement is not true about the data set when the new score of 84 is included, let's analyze the implications of adding this score to the existing data set.
1. **The mean score increases.**
Adding a score of 84 (which is higher than the existing maximum score of 82) will generally increase the mean. So this statement is true.
2. **The interquartile range of the scores decreases.**
The interquartile range (IQR) is determined by the difference between the first quartile (Q1) and the third quartile (Q3). Since the highest score (84) does not affect the middle 50% of the data, and it is already at the higher end, the IQR may not necessarily decrease. In fact, adding 84 could potentially increase the range of the upper quartile, but it’s difficult to definitively state without the original data points. This statement is questionable and may not be true.
3. **The standard deviation of the scores increases.**
Adding a score further away from the existing scores (which 84 would be, given the existing scores do not go that high) would increase the spread of the data. Therefore, this statement is true.
4. **The median score stays the same.**
Since the original median score would likely have been in the middle of the existing scores (likely around 78), adding an additional high score of 84 will not change the central tendency of the data significantly. Hence, this statement is also likely true.
Given the analysis, the statement that **"The interquartile range of the scores decreases."** is not necessarily true and is the most likely candidate for the statement that is false as adding the high score does not guarantee a decrease in the IQR.
1. **The mean score increases.**
Adding a score of 84 (which is higher than the existing maximum score of 82) will generally increase the mean. So this statement is true.
2. **The interquartile range of the scores decreases.**
The interquartile range (IQR) is determined by the difference between the first quartile (Q1) and the third quartile (Q3). Since the highest score (84) does not affect the middle 50% of the data, and it is already at the higher end, the IQR may not necessarily decrease. In fact, adding 84 could potentially increase the range of the upper quartile, but it’s difficult to definitively state without the original data points. This statement is questionable and may not be true.
3. **The standard deviation of the scores increases.**
Adding a score further away from the existing scores (which 84 would be, given the existing scores do not go that high) would increase the spread of the data. Therefore, this statement is true.
4. **The median score stays the same.**
Since the original median score would likely have been in the middle of the existing scores (likely around 78), adding an additional high score of 84 will not change the central tendency of the data significantly. Hence, this statement is also likely true.
Given the analysis, the statement that **"The interquartile range of the scores decreases."** is not necessarily true and is the most likely candidate for the statement that is false as adding the high score does not guarantee a decrease in the IQR.