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
First, we need to find the medians of each class. To do this, we need to put the data in order from least to greatest:
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
For Class 1, the median is the middle number, which is 8.
For Class 2, there are 15 numbers, so the median is the average of the two middle numbers: (7+8)/2 = 7.5
The difference between the medians is 8 - 7.5 = 0.5. Therefore, Class 1 has a higher median by 0.5 miles per week.