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?

Question

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

Answer 1

To find the median differences between the two classes, we first need to calculate the median for each class.

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

1. Sort the data: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
2. Count the number of values: 15 (odd)
3. The median is the middle number:
   • The median position is at (15 + 1) / 2 = 8.
   • The 8th number in the sorted list is 8.

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

1. Sort the data: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
2. Count the number of values: 15 (odd)
3. The median is the middle number:
   • The median position is at (15 + 1) / 2 = 8.
   • The 8th number in the sorted list is 7.

Comparing the Medians:

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

The difference between the medians is: \[ 8 - 7 = 1 \]

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