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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]
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