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

Responses

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

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.

1 answer

To find the medians of both classes, we first need to list the data in ascending order and then determine the median.

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

Since there are 15 numbers (an odd number), the median is the middle number:

  • Median of Class 1 = 8 (the 8th number in the ordered list).

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

Again, there are 15 numbers (an odd number), so the median is the middle number:

  • Median of Class 2 = 7 (the 8th number in the ordered list).

Now, we compare the medians:

  • Median of Class 1 = 8
  • Median of Class 2 = 7

The difference between the medians is: 8 - 7 = 1 mile.

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

So the correct response is: Class 1 has a higher median than Class 2 by 1 mile.