The ages of students enrolled in two math classes at the local community college, Class A and Class B, are listed in order below. Determine which of the following statements is true about Class B.

Question

Class A: 20, 20, 20, 21, 22, 23, 23, 25, 27, 29, 30, 31, 34, 35, 36, 39, 40

Class B: 16, 17, 18, 18, 20, 22, 22, 24, 26, 26, 28, 29, 30, 34, 37, 40, 42

A. 
Class B has a larger median and a larger interquartile range.

B. 
Class B has a larger median and the same interquartile range.

C. 
Class B has a smaller median and a larger interquartile range.

D. 
Class B has a smaller median and the same interquartile range.

GPT-4o mini · Answer

To compare the statistical properties of Class A and Class B, we first need to compute the median and interquartile range (IQR) for both classes.

Class A

Ages: 20, 20, 20, 21, 22, 23, 23, 25, 27, 29, 30, 31, 34, 35, 36, 39, 40

Median:

Class A has 17 students (an odd number), thus the median is the age of the 9th student in the ordered list.
The 9th student is 27.
Median of Class A = 27

Interquartile Range (IQR):

To find the IQR, we need Q1 (1st quartile) and Q3 (3rd quartile).
Q1 is the median of the first half (first 8 values): 20, 20, 20, 21, 22, 23, 23, 25.
The median of these values (4th + 5th values) is (21 + 22) / 2 = 21.5.
Q1 = 21.5.
Q3 is the median of the second half (last 8 values): 29, 30, 31, 34, 35, 36, 39, 40.
The median of these values (4th + 5th values) is (34 + 35) / 2 = 34.5.
Q3 = 34.5.
IQR = Q3 - Q1 = 34.5 - 21.5 = 13.

Class B

Ages: 16, 17, 18, 18, 20, 22, 22, 24, 26, 26, 28, 29, 30, 34, 37, 40, 42

Median:

Class B has 17 students (an odd number), thus the median is the age of the 9th student in the ordered list.
The 9th student is 26.
Median of Class B = 26

Interquartile Range (IQR):

Q1 is the median of the first half (first 8 values): 16, 17, 18, 18, 20, 22, 22, 24.
The median of these values (4th + 5th values) is (18 + 20) / 2 = 19.
Q1 = 19.
Q3 is the median of the second half (last 8 values): 26, 26, 28, 29, 30, 34, 37, 40, 42.
The median of these values (4th + 5th values) is (29 + 30) / 2 = 29.5.
Q3 = 29.5.
IQR = Q3 - Q1 = 29.5 - 19 = 10.5.

Summary

Median of Class A: 27
Median of Class B: 26
IQR of Class A: 13
IQR of Class B: 10.5

Conclusion

Class B has a smaller median (26 < 27) and a smaller interquartile range (10.5 < 13).

The correct answer is D. Class B has a smaller median and the same interquartile range.

In this case, the interquartile ranges are not the same; they actually are 13 for Class A and 10.5 for Class B. So after careful consideration, the true statement about Class B is:

Class B has a smaller median and a smaller interquartile range. It looks like the options provided include a choice that assumes identical ranges which doesn't hold true in this case.

Thus, none of the options are perfectly correct. However, if the interquartile comparison leads to no distinct class choice, it suggests that the majority test would indicate Class B has a smaller Median as opposed to suggesting anything higher.

Confirming, Class B has a smaller median but also a smaller IQR than Class A. Hence all statements would be technically invalid from an option selection in its current locked state.