Question

alanna compared her science and math test grades. her results are shown below.
math: 84, 82, 95, 87, 93, 88, 81, 94, 90
science: 72, 75, 82, 76, 85, 77, 76, 75, 79
which statement describes the data sets?
a. the median of her math grades is larger than that of her science grades, but the interquartile range of her science grades is larger than that of her math grades.
b. the median of her science grades is larger than that of her math grades, but the interquartile range of her math grades is larger than that of her science grades.
c. both the median and interquartile range of her math grades are larger than those of her science grades.
d. both the median and interquartile range of her science grades are larger than those of her math grades.

Explanation:

Step1: Sort the data

Math: \(64,62,95,87,93,88,41,94,90\) sorted is \(41,62,64,87,88,90,93,94,95\)
Science: \(72,75,82,76,82,87,78,75,79\) sorted is \(72,75,75,76,78,79,82,82,87\)

Step2: Calculate the median

For math (9 data points), median is the 5th - value: \(88\)
For science (9 data points), median is the 5th - value: \(78\)

Step3: Calculate the interquartile range (IQR)

For math:
First quartile \(Q_1\) (average of 2nd and 3rd - value): \(\frac{62 + 64}{2}=63\)
Third quartile \(Q_3\) (average of 7th and 8th - value): \(\frac{93+94}{2}=93.5\)
\(IQR = 93.5 - 63=30.5\)
For science:
First quartile \(Q_1\) (average of 2nd and 3rd - value): \(\frac{75 + 75}{2}=75\)
Third quartile \(Q_3\) (average of 7th and 8th - value): \(\frac{82+82}{2}=82\)
\(IQR = 82 - 75 = 7\)

Answer:

A. The median of her math grades is larger than that of her science grades, but the interquartile range of her science grades is larger than that of her math grades.