Question

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?%0D%0A%0D%0AClass 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11%0D%0AClass 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AClass 2 has a higher median than Class 1 by 0.5 mile.%0D%0AClass 2 has a higher median than Class 1 by 0.5 mile.%0D%0A%0D%0AClass 1 has a higher median than Class 2 by 1 mile.%0D%0AClass 1 has a higher median than Class 2 by 1 mile.%0D%0A%0D%0AClass 2 has a higher median than Class 1 by 1 mile.%0D%0AClass 2 has a higher median than Class 1 by 1 mile.%0D%0A%0D%0AClass 1 has a higher median than Class 2 by 0.5 mile.

Answer 1

To find the median for each class, we first need to order the data points:
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 value, which is the 8th value in the ordered list, so the median for Class 1 is 8.

For Class 2, there are 15 data points, so the median is the average of the 8th and 9th values (since 7 and 8 are in the middle), which is (7+8)/2 = 7.5.

The difference between the medians is 7.5 - 8 = -0.5. Since the median for Class 2 is 7.5, which is 0.5 miles higher than the median for Class 1, we conclude that Class 2 has a higher median by 0.5 miles.