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
(1 point)
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
To find the median, we look for the middle value. If there are an even number of values, we take the average of the two middle values.
Class 1: Median is (8+10)/2 = 9
Class 2: Median is 7
The difference between the medians is 9-7 = 2. Therefore, class 1 has a higher median by 2 miles per week.
To find the median, we need to first arrange the data in ascending order:
For Class 1:
2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
For Class 2:
4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
The medians for the two classes are the middle values of the data sets:
For Class 1, the median is 8.
For Class 2, the median is 7.
To find the difference between the medians:
8 - 7 = 1
Therefore, Class 1 has a higher median by 1 mile.