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
First, let's order the data 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
To find the median, we need to find the middle value. If there are an odd number of values, this will be the exact middle value. If there are an even number of values, we need to take the average of the two middle values.
For Class 1, we have an odd number of values, so the median is the middle value: 5.
For Class 2, we have an even number of values, so we need to find the average of the two middle values: (4 + 5) / 2 = 4.5.
Therefore, Class 1 has a higher median number of books read (5) than Class 2 (4.5).
To find the median number of books read by each class, we need to arrange the data in each class in ascending order and then find the middle value.
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
Now, let's find the median for each class.
For Class 1, the median is the middle value, which is the value at the 8th position in the ordered list of data. The value at the 8th position is 5.
For Class 2, the median is also the middle value, which is the value at the 8th position in the ordered list of data. The value at the 8th position is 3.
Therefore, the median number of books read by Class 1 is 5, and the median number of books read by Class 2 is 3.
Since 5 is greater than 3, Class 1 has a higher median number of books read than Class 2.