The table below shows the quiz grades for two students.
Drew 90 81 86 79 97 84 92
Nancy 96 68 91 94 69 99 92
Which statement is true about the data above?
A.
The students' grades have the same interquartile range, but Nancy has a higher mean.
B.
The students have the same mean, but Drew's quiz grades have a higher interquartile range.
C.
The students' grades have the same interquartile range, but Drew has a higher mean.
D.
The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
C. The students' grades have the same interquartile range, but Drew has a higher mean.
To determine which statement is true about the data above, we need to compare the interquartile range and the mean for both students.
The interquartile range is a measure of the spread or variability in a set of data and is calculated as the difference between the first quartile (Q1) and the third quartile (Q3) in the data set.
For Drew:
Q1 = 81
Q3 = 92
Interquartile range = Q3 - Q1 = 92 - 81 = 11
For Nancy:
Q1 = 69
Q3 = 96
Interquartile range = Q3 - Q1 = 96 - 69 = 27
Now let's compare the means:
For Drew:
Mean = (90 + 81 + 86 + 79 + 97 + 84 + 92) / 7 = 609 / 7 ≈ 87
For Nancy:
Mean = (96 + 68 + 91 + 94 + 69 + 99 + 92) / 7 = 609 / 7 ≈ 87
Comparing the interquartile ranges, we see that Drew's interquartile range is 11 and Nancy's interquartile range is 27. Nancy's interquartile range is higher.
Comparing the means, we see that both students have the same mean of approximately 87.
Therefore, the correct statement is:
D. The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
To determine the mean and interquartile range for each student, we need to calculate these statistics.
Mean:
To find the mean (average) for each student, we add up all their quiz grades and divide by the number of quizzes they took.
For Drew:
Mean = (90 + 81 + 86 + 79 + 97 + 84 + 92)/7 = 609/7 ≈ 87
For Nancy:
Mean = (96 + 68 + 91 + 94 + 69 + 99 + 92)/7 = 609/7 ≈ 87
Interquartile Range:
The interquartile range (IQR) is a measure of the spread of the data. To calculate the IQR, we need to first determine the first quartile (Q1) and the third quartile (Q3).
For Drew:
Q1 = 81 (the median of the lower half of the data)
Q3 = 92 (the median of the upper half of the data)
IQR = Q3 - Q1 = 92 - 81 = 11
For Nancy:
Q1 = 69
Q3 = 96
IQR = Q3 - Q1 = 96 - 69 = 27
Now, let's compare the statements:
A. The students' grades have the same interquartile range, but Nancy has a higher mean.
False. The students have different means, but we calculated that Drew and Nancy have the same mean of approximately 87.
B. The students have the same mean, but Drew's quiz grades have a higher interquartile range.
False. The interquartile range for Nancy is 27, which is greater than Drew's interquartile range of 11.
C. The students' grades have the same interquartile range, but Drew has a higher mean.
False. Drew and Nancy do not have the same mean, but we calculated that they have the same mean of approximately 87.
D. The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
True. We determined that both students have the same mean of approximately 87, but Nancy has a higher interquartile range of 27 compared to Drew's interquartile range of 11.
Therefore, the correct statement is:
D. The students have the same mean, but Nancy's quiz grades have a higher interquartile range.