(c) Find the third quartile of the above data. 87 88.5 057 58.5
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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![### Determining the Third Quartile from a Data Set
**Problem Statement**: The test scores of 16 students are listed below:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
**Question**: Find the third quartile of the above data.
**Options**:
- A. 87
- B. 88.5
- C. 57
- D. 58.5
**Solution Explanation**:
To find the third quartile (Q3) of a data set, follow these steps:
1. **Arrange the Data in Ascending Order**:
The data provided is already in ascending order:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97
2. **Determine the Position of the Third Quartile**:
The third quartile (Q3) is the median of the upper half of the data. Since there are 16 data points, the upper half begins at the 9th data point and ends at the 16th data point.
Upper half: 75, 76, 85, 87, 90, 94, 95, 97
3. **Find the Median of the Upper Half**:
The median of these 8 values is the average of the 4th and 5th values (87 and 90):
\[
Q3 = \frac{87 + 90}{2} = 88.5
\]
Therefore, the third quartile (Q3) of the given data set is **88.5**.
**Correct Answer**: B. 88.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9b814ac-1a5f-4504-b547-b7326372e811%2Fdbb39a23-11c3-4553-9e5f-27c7eaa1843c%2Fke2zqlq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Third Quartile from a Data Set
**Problem Statement**: The test scores of 16 students are listed below:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
**Question**: Find the third quartile of the above data.
**Options**:
- A. 87
- B. 88.5
- C. 57
- D. 58.5
**Solution Explanation**:
To find the third quartile (Q3) of a data set, follow these steps:
1. **Arrange the Data in Ascending Order**:
The data provided is already in ascending order:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97
2. **Determine the Position of the Third Quartile**:
The third quartile (Q3) is the median of the upper half of the data. Since there are 16 data points, the upper half begins at the 9th data point and ends at the 16th data point.
Upper half: 75, 76, 85, 87, 90, 94, 95, 97
3. **Find the Median of the Upper Half**:
The median of these 8 values is the average of the 4th and 5th values (87 and 90):
\[
Q3 = \frac{87 + 90}{2} = 88.5
\]
Therefore, the third quartile (Q3) of the given data set is **88.5**.
**Correct Answer**: B. 88.5
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