The data shows the number of miles run per week by randomly selected students from two different classes. Find the difference between the medians. Which class has a higher median? By how much?

Question

Class 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Class 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10

(1 point)
Responses

Class 2 has a higher median than Class 1 by 0.5 mile.
Class 2 has a higher median than Class 1 by 0.5 mile.

Class 1 has a higher median than Class 2 by 0.5 mile.
Class 1 has a higher median than Class 2 by 0.5 mile.

Class 2 has a higher median than Class 1 by 1 mile.
Class 2 has a higher median than Class 1 by 1 mile.

Class 1 has a higher median than Class 2 by 1 mile

:)

Answer 1

To find the medians of each class, we first need to order the data points from least to greatest for each class and then find their respective medians.

Class 1: Data: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11 Ordered Data: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14

Since there are 15 data points in Class 1 (an odd number), the median is the middle value, which is the 8th value in the ordered list. Median of Class 1 = 8

Class 2: Data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10 Ordered Data: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12

Similarly, for Class 2 (also an odd number of data points, 15), the median is the 8th value in the ordered list. Median of Class 2 = 7

Finding the Difference: Median of Class 1 - Median of Class 2 = 8 - 7 = 1

Conclusion: Class 1 has a higher median than Class 2 by 1 mile. The correct response is:

Class 1 has a higher median than Class 2 by 1 mile.