Fifteen students are randomly selected from two different classes. They were asked how many books they read during the summer. Their responses are as follows. Find the median number of books read by each class. Which class has a higher median number of books read?
Class 1: 0, 5, 3, 6, 7, 8, 10, 1, 1, 4, 5, 6, 4, 5, 6
Class 2: 2, 2, 4, 3, 0, 0, 6, 7, 10, 9, 6, 5, 3, 1, 2
The median number of books read during the summer by Class 1 is
.
The median number of books read during the summer by Class 2 is
.
Class
has a higher median number of books read during the summer.
To find the median, we first need to put the data in order from least to greatest:
Class 1: 0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10
Class 2: 0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 9, 10
For Class 1, the median is the middle number, which is 5.
For Class 2, there are two middle numbers (4 and 5). In this case, we take the average of the two middle numbers to find the median, which is (4+5)/2 = 4.5.
Therefore, Class 1 has a higher median number of books read during the summer.
Now are you sure that is correct?
I apologize, I made a mistake in my previous response. After sorting the data, we have:
Class 1: 0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10
Class 2: 0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 9, 10
For Class 1, there are an odd number of data points, so the median is the middle value, which is 5.
For Class 2, there are an even number of data points, so the median is the average of the two middle values, which are 4 and 5. Therefore, the median for Class 2 is (4 + 5)/2 = 4.5.
Therefore, Class 1 and Class 2 have the same median number of books read during the summer.
To find the median number of books read by each class, we need to first sort the responses in ascending order.
For Class 1:
0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10.
For Class 2:
0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 9, 10.
Now, let's find the median for each class.
For Class 1:
We have 15 responses, which is an odd number. The median is the middle value, which is the 8th number in the sorted list. Therefore, the median number of books read by Class 1 is 5.
For Class 2:
We also have 15 responses, which is an odd number. The median is the middle value, which is the 8th number in the sorted list. Therefore, the median number of books read by Class 2 is 3.
Class 1 has a higher median number of books read during the summer.