Select the correct answer.

The number of books checked out at two different libraries each day this week is shown below.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
& Mon. & Tues. & Wed. & Thurs. & Fri. & Sat. \\
\hline
Williams & 63 & 56 & 60 & 55 & 62 & 55 \\
\hline
Ryder & 80 & 75 & 82 & 84 & 82 & 79 \\
\hline
\end{tabular}

How do the median number of books checked out each day compare?

A. The median number of books checked out at Ryder is 18 more than the median number of books checked out at Williams.

B. The median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.

C. The median number of books checked out at Williams is 25 more than the median number of books checked out at Ryder.

D. The median number of books checked out at Ryder is equal to the median number of books checked out at Williams.



Answer :

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.