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

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

1 answer

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

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: There are 15 data points (odd number).

  3. Find the median: The median is the middle value, which is the 8th value in the sorted list:

    • Median for Class 1 = 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: There are 15 data points (odd number).

  3. Find the median: The median is again the middle value, which is the 8th value in the sorted list:

    • Median for Class 2 = 7

Finding the difference between the medians:

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

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

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.