To determine how the median number of books checked out each day at the two libraries compare, we first need to calculate the median for each library.
### Williams Library:
The number of books checked out each day at Williams is:
[tex]\[ 63, 56, 60, 55, 62, 55 \][/tex]
1. Sort the data:
[tex]\[ 55, 55, 56, 60, 62, 63 \][/tex]
2. Calculate the median:
- Since there are 6 data points, the median is the average of the 3rd and 4th values.
- The 3rd value is [tex]\(56\)[/tex] and the 4th value is [tex]\(60\)[/tex].
[tex]\[ \text{Median}_\text{Williams} = \frac{56 + 60}{2} = \frac{116}{2} = 58 \][/tex]
### Ryder Library:
The number of books checked out each day at Ryder is:
[tex]\[ 80, 75, 82, 84, 82, 79 \][/tex]
1. Sort the data:
[tex]\[ 75, 79, 80, 82, 82, 84 \][/tex]
2. Calculate the median:
- Since there are 6 data points, the median is the average of the 3rd and 4th values.
- The 3rd value is [tex]\(80\)[/tex] and the 4th value is [tex]\(82\)[/tex].
[tex]\[ \text{Median}_\text{Ryder} = \frac{80 + 82}{2} = \frac{162}{2} = 81 \][/tex]
### Comparison:
We now compare the medians of the two libraries.
- Median at Williams: [tex]\( 58 \)[/tex]
- Median at Ryder: [tex]\( 81 \)[/tex]
The difference between the medians is:
[tex]\[ 81 - 58 = 23 \][/tex]
Therefore, the median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.
The correct answer is:
B. The median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.
