Problem
The ratings for the ten leading passers in a football league for a particular season are ranked in the table shown. Find the third decile for the league. What is the third decile? (Type an integer or a decimal.) \begin{tabular}{ccc} Rank & Passer & Rating points \\ 1 & Passer 1 & 76.6 \\ 2 & Passer 2 & 71.2 \\ 3 & Passer 3 & 68.3 \\ 4 & Passer 4 & 66.9 \\ 5 & Passer 5 & 64.2 \\ 6 & Passer 6 & 63.7 \\ 7 & Passer 7 & 63.2 \\ 8 & Passer 8 & 61.6 \\ 9 & Passer 9 & 59.0 \\ 10 & Passer 10 & 58.3 \end{tabular}
Solution
Step 1 ：The third decile (D3) is the 30th percentile of the data set. Since we have 10 data points, the 30th percentile would fall between the 3rd and 4th data points.
Step 2 ：We can calculate the third decile by taking the average of the 3rd and 4th data points.
Step 3 ：The ratings for the ten leading passers are [76.6, 71.2, 68.3, 66.9, 64.2, 63.7, 63.2, 61.6, 59.0, 58.3].
Step 4 ：The third decile is calculated as \( \frac{68.3 + 66.9}{2} = 67.6 \).
Step 5 ：Final Answer: The third decile is \(\boxed{67.6}\).
