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)
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 1 mile.
Class 2 has a higher median than Class 1 by 1 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 0.5 mile.

1 answer

To find the difference between the medians of the two classes, we first need to calculate the medians for both Class 1 and Class 2.

Here's the data for each class:

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

Step 1: Sort the data for both classes

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

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

Step 2: Find the median for Class 1

Class 1 has 15 data points (odd number), so the median is the middle value:

  • Middle position: \( (15 + 1) / 2 = 8 \)

The 8th value in the sorted list is:

  • Median of Class 1 = 8

Step 3: Find the median for Class 2

Class 2 also has 15 data points (odd number), so the median is the middle value:

  • Middle position: \( (15 + 1) / 2 = 8 \)

The 8th value in the sorted list is:

  • Median of Class 2 = 7

Step 4: Calculate the difference between the medians

Now, we find the difference in the medians:

  • Difference = Median of Class 1 - Median of Class 2
  • Difference = 8 - 7 = 1 mile

Conclusion:

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

Therefore, the correct response is:

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