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 arrange 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
Now we find the middle value(s) of each set of data. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
For Class 1, there are 15 values, so the median is the average of the 7th and 8th values:
median = (5+5)/2 = 5
For Class 2, there are also 15 values, so the median is the average of the 8th and 9th values:
median = (3+4)/2 = 3.5
Therefore, Class 1 has a higher median number of books read during the summer.
To find the median number of books read by each class, we need to arrange the responses in ascending order and find the middle value.
Arranging the responses in ascending order for Class 1:
0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10
Counting the number of responses, we see that there are 15 values. Since the number of values is odd, the median will be the middle value, which is the 8th value: 5.
Therefore, the median number of books read during the summer by Class 1 is 5.
Arranging the responses in ascending order for Class 2:
0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 9, 10
Again, counting the number of responses, we see that there are 15 values. As the number of values is odd, the median will be the middle value, which is the 8th value: 3.
Therefore, the median number of books read during the summer by Class 2 is 3.
Comparing the medians:
Class 1's median: 5
Class 2's median: 3
The class with a higher median number of books read during the summer is Class 1.