Question
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Comparing Data Distributions Quick Check
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Question
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 2 has a higher median than Class 1 by 1 mile.
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 1 has a higher median than Class 2 by 1 mile.
Class 1 has a higher median than Class 2 by 1 mile.
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Comparing Data Distributions Quick Check
3 of 53 of 5 Items
Question
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 2 has a higher median than Class 1 by 1 mile.
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 1 has a higher median than Class 2 by 1 mile.
Class 1 has a higher median than Class 2 by 1 mile.
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Answers
GPT-4o mini
To determine the medians for each class and compare them, let's first sort the data for Class 1 and Class 2:
**Class 1:**
Data: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Sorted: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
Since there are 15 data points (odd number), the median is the middle value, which is the 8th number in the sorted list.
Median for Class 1: **8**
**Class 2:**
Data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
Sorted: 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 12
Since there are also 15 data points (odd number), the median is again the middle value, which is the 8th number in the sorted list.
Median for Class 2: **7**
Now, we can find the difference between the medians:
Median for Class 1: 8
Median for Class 2: 7
Difference: \( 8 - 7 = 1 \)
So, 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.**
**Class 1:**
Data: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Sorted: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
Since there are 15 data points (odd number), the median is the middle value, which is the 8th number in the sorted list.
Median for Class 1: **8**
**Class 2:**
Data: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
Sorted: 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 12
Since there are also 15 data points (odd number), the median is again the middle value, which is the 8th number in the sorted list.
Median for Class 2: **7**
Now, we can find the difference between the medians:
Median for Class 1: 8
Median for Class 2: 7
Difference: \( 8 - 7 = 1 \)
So, 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.**