The ratings for the ten leading passers in the league for the 2009 regular season are ranked in the table below. Construct a box plot for the rating points data.

[tex]
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Rank} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
\text{NFL Passer} & A & B & C & D & E & F & G & H & I & J \\
\hline
\text{Rating Points} & 92.3 & 96.3 & 97.8 & 98.2 & 99.6 & 100.8 & 103.3 & 104.5 & 105.8 & 109.6 \\
\hline
\end{array}
\]
[/tex]

Choose the correct graph below.

A.
[tex]
\[
\begin{array}{l}
Q_1=96.3, Q_2=98.2 \\
Q_3=100.8
\end{array}
\]
[/tex]

B.
[tex]
\[
Q_1=97.8, Q_2=100.2 \\
Q_3=104.5
\]
[/tex]

C.
[tex]
\[
\begin{array}{l}
Q_1=98.2, Q_2=100.8 \\
Q_3=105.8
\end{array}
\]
[/tex]

To construct a box plot for the given rating points data, we need to find the quartiles: Q1 (the first quartile), Q2 (the median), and Q3 (the third quartile). Here are the steps:

1. List the Rating Points in Ascending Order:
- The data given is already in ascending order: 92.3, 96.3, 97.8, 98.2, 99.6, 100.8, 103.3, 104.5, 105.8, 109.6.

2. Find the Median (Q2):
- Since there are 10 data points (an even number), the median is the average of the 5th and 6th values.
- The 5th value is 99.6, and the 6th value is 100.8.
- Median (Q2) = (99.6 + 100.8) / 2 = 100.2

3. Find the First Quartile (Q1):
- Q1 is the median of the first half of the data. Consider the first five numbers: 92.3, 96.3, 97.8, 98.2, 99.6.
- The median of this subset is the 3rd value: 97.8.

4. Find the Third Quartile (Q3):
- Q3 is the median of the second half of the data. Consider the last five numbers: 100.8, 103.3, 104.5, 105.8, 109.6.
- The median of this subset is the 3rd value: 104.5.

With these calculated quartiles: Q1 = 97.8, Q2 = 100.2, and Q3 = 104.5, we can match them to the provided options for constructing the box plot. The correct option is:

B.
[tex]$ Q_1 = 97.8, Q_2 = 100.2, Q_3 = 104.5 $[/tex]