Problem

The ratings for the ten leading passers in the league for 2009 regular season play are ranked in the table. Construct a box plot for the rating points data.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline Rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline NFL Passer & A & B & C & D & E & F & G & H & I & J \\
\hline Rating Points & 93.2 & 96.7 & 97.7 & 98.7 & 99.5 & 101.5 & 103.7 & 104.7 & 107.3 & 109.9 \\
\hline
\end{tabular}
Choose the correct graph below.
A.
\[
\begin{array}{l}
Q_{1}=97.7, Q_{2}=100.5, \\
Q_{3}=104.7
\end{array}
\]
B.
\[
\begin{array}{l}
Q_{1}=98.7, Q_{2}=101.5 \\
Q_{3}=107.3
\end{array}
\]
C.
\[
\begin{array}{l}
Q_{1}=96.7, Q_{2}=98.7 \\
Q_{3}=101.5
\end{array}
\]

Answer

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Answer

Final Answer: The correct graph is not listed among the options. The calculated quartiles are \(Q_{1}=97.95\), \(Q_{2}=100.5\), and \(Q_{3}=104.45\). None of the provided options match these values. So, \(\boxed{\text{The correct graph is not listed among the options.}}\)

Steps

Step 1 :The problem is asking for a box plot of the rating points data. A box plot is a graphical representation of statistical data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

Step 2 :To answer this question, we need to calculate the quartiles of the data. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the median of the whole data set, and the third quartile (Q3) is the median of the upper half of the data.

Step 3 :Given rating points are [93.2, 96.7, 97.7, 98.7, 99.5, 101.5, 103.7, 104.7, 107.3, 109.9].

Step 4 :Calculate the quartiles: Q1 = 97.95, Q2 = 100.5, Q3 = 104.45.

Step 5 :Final Answer: The correct graph is not listed among the options. The calculated quartiles are \(Q_{1}=97.95\), \(Q_{2}=100.5\), and \(Q_{3}=104.45\). None of the provided options match these values. So, \(\boxed{\text{The correct graph is not listed among the options.}}\)

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