Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
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]
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]
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
