Da data shows da number of miles run per week by randomly selected students from 2 different classes. Find da difference between 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
Claws 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 4, 10

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

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

C ) Class 2 has a higher median dan class 1 by 1 mile

D ) Class 1 has a higher median Dan class 2 by 1 mile

Answer 1

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

Class 1 Data:

Original 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

The number of data points (n) for Class 1 is 15 (an odd number), so the median is the middle value.

• The middle index is \( \frac{15 + 1}{2} = 8 \).
• The 8th value in the sorted list is 8.

Median of Class 1 = 8

Class 2 Data:

Original data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 4, 10

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

The number of data points (n) for Class 2 is 14 (an even number), so the median is the average of the two middle values.

• The middle indices are \( \frac{14}{2} = 7 \) and \( 8 \).
• The 7th value is 8 and the 8th value is 8.

Median of Class 2 = \( \frac{8 + 8}{2} = 8 \)

Difference Between Medians:

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

The difference between the medians is: \( 8 - 8 = 0 \)

Since both medians are equal, neither class has a higher median.

Conclusion

All options imply one class has a higher median, which is incorrect. The medians are equal. Therefore, none of the provided options A, B, C, or D is correct.