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 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 1 mile.
Class 2 has a higher median than Class 1 by 0.5 mile.
Class 1 has a higher median than Class 2 by 1 mile.
are you sure?
To find the medians of the two classes, we first need to arrange the data in ascending order:
Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14.
Class 2: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12.
Now we can find the medians. Since both classes have an odd number of data points, the median is the middle value.
For Class 1, the median is the 8th value, which is 8.
For Class 2, the median is the 8th value, which is 7.
Therefore, the difference between the medians is 8 - 7 = 1 mile.
Hence, the correct answer is: Class 1 has a higher median than Class 2 by 1 mile.
To find the difference between medians and determine which class has a higher median, we need to calculate the medians for each class.
First, let's find the median for Class 1:
1. Arrange the numbers in the data set in ascending order: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14.
2. Since there are 15 numbers in the data set, the median will be the middle number. In this case, the middle number is the 8th number, which is 8.
Now, let's find the median for Class 2:
1. Arrange the numbers in the data set in ascending order: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12.
2. Since there are 15 numbers in the data set, the median will be the middle number. In this case, the middle number is the 8th number, which is 8.
Now that we have the medians for both classes, we can calculate the difference:
Median of Class 2 - Median of Class 1 = 8 - 8 = 0.
This means that the difference between the medians is 0, indicating that both classes have the same median.
Therefore, none of the given options is correct.