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

1 answer

To find the medians of the two classes, we first need to sort the data for each class and then calculate the median.

Class 1: Data: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Sorted Data: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
To find the median:

  • There are 15 values (odd number).
  • The median is the middle value, which is the 8th value in the sorted list.

Median of Class 1 = 8

Class 2: Data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
Sorted Data: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
To find the median:

  • There are 15 values (odd number).
  • The median is the middle value, which is the 8th value in the sorted list.

Median of Class 2 = 7

Calculating the difference between the medians:

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

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

The answer is: Class 1 has a higher median than Class 2 by 1 mile.