Question
Jim recorded the points a group of students scored during a gaming session in the dot plot below.
plot line labeled 0-0 howver the only plots are 0 5 and 10
2 has 1
6 has 3
7 has 3
8 has 2
9 has 1
every other spot is empty
Which measure of center would be best to use for this distribution?
A.
mode
B.
mean
C.
interquartile range
D.
median
plot line labeled 0-0 howver the only plots are 0 5 and 10
2 has 1
6 has 3
7 has 3
8 has 2
9 has 1
every other spot is empty
Which measure of center would be best to use for this distribution?
A.
mode
B.
mean
C.
interquartile range
D.
median
Answers
GPT-4o mini
To determine which measure of center is best to use for the given distribution, we can analyze the data points from the dot plot you described. The scores recorded are:
- 0 (1 student)
- 5 (0 students)
- 6 (3 students)
- 7 (3 students)
- 8 (2 students)
- 9 (1 student)
- 10 (0 students)
Since the mode (most frequent score) is 6 and 7 (both appear 3 times), it could be a good measure to report since it reflects the most common scores.
The mean (average) may not accurately represent the center of the distribution given that there is a score of 0 present, which could skew the average downward.
The median (the middle value when scores are ordered) could provide a value you can calculate from the list but would also depend on how many total scores there are. In this case, the scores would be ordered as follows: 0, 6, 6, 6, 7, 7, 7, 8, 8, 9. The median would be the average of the 5th and 6th scores, which are both 7, thus the median is 7.
The interquartile range (IQR) is more about variability rather than a measure of central tendency, so it wouldn't apply here.
Based on these considerations, the best measure of center to describe this distribution is:
**A. mode**, since it reflects the most frequently occurring scores accurately without being skewed by the outlier (the score of 0).
- 0 (1 student)
- 5 (0 students)
- 6 (3 students)
- 7 (3 students)
- 8 (2 students)
- 9 (1 student)
- 10 (0 students)
Since the mode (most frequent score) is 6 and 7 (both appear 3 times), it could be a good measure to report since it reflects the most common scores.
The mean (average) may not accurately represent the center of the distribution given that there is a score of 0 present, which could skew the average downward.
The median (the middle value when scores are ordered) could provide a value you can calculate from the list but would also depend on how many total scores there are. In this case, the scores would be ordered as follows: 0, 6, 6, 6, 7, 7, 7, 8, 8, 9. The median would be the average of the 5th and 6th scores, which are both 7, thus the median is 7.
The interquartile range (IQR) is more about variability rather than a measure of central tendency, so it wouldn't apply here.
Based on these considerations, the best measure of center to describe this distribution is:
**A. mode**, since it reflects the most frequently occurring scores accurately without being skewed by the outlier (the score of 0).