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?
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
A. Class 1 has a higher median than class 2 by 0.5 mile
B. Class 1 has higher median that class 2 by 1 mile
C. Class 2 has a higher median than class 1 by 1 mile
D. Class 2 has a higher median than class 1 by 0.5 mile
To find the medians, we need to first sort the data sets in increasing order:
Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
Class 2: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
Both data sets have 15 values, so we can find the median by taking the average of the middle two values.
For Class 1: Median = (7 + 8)/2 = 7.5
For Class 2: Median = (7 + 8)/2 = 7.5
The medians for both classes are equal, so neither class has a higher median than the other. The difference between the medians is 0. Therefore, the correct answer is:
D. Class 2 has a higher median than class 1 by 0.5 mile.