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
a Class 1 has a higher median than Class 2 by 0.5 mile.
b Class 2 has a higher median than Class 1 by 1 mile.
c Class 1 has a higher median than Class 2 by 1 mile.
d Class 2 has a higher median than Class 1 by 0.5 mile.
To find the median, we need to first order the data from least to greatest:
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
Class 1 has 15 students, so we take the middle two values and find their average:
Median of Class 1: (8 + 10)/2 = 9
Class 2 also has 15 students, so we take the middle value:
Median of Class 2: 7
The difference between the medians is:
9 - 7 = 2
Therefore, Class 1 has a higher median than Class 2. The answer is c) Class 1 has a higher median than Class 2 by 1 mile.
To find the medians of the two classes, we need to sort the data sets 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
Since both data sets have an odd number of values, the median is simply the middle value in each set. In this case:
Class 1 median = 8
Class 2 median = 7
To find the difference between the medians, subtract the median of Class 2 from the median of Class 1:
8 - 7 = 1
So the difference between the medians is 1 mile. Since the median of Class 1 is higher than the median of Class 2, the answer is (c) Class 1 has a higher median than Class 2 by 1 mile.