The following are the ages of 12 music teachers in a school district. 31, 33, 36, 38, 39, 40, 40, 42, 43, 50, 52, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
The following are the ages of 12 music teachers in a school district. 31, 33, 36, 38, 39, 40, 40, 42, 43, 50, 52, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
MATLAB: An Introduction with Applications
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![### Ages of Music Teachers Analysis
The following data set represents the ages of 12 music teachers in a school district:
\[ 31, 33, 36, 38, 39, 40, 40, 42, 43, 50, 52, 56 \]
These ages are arranged in ascending order. The task is to determine the five-number summary and the interquartile range (IQR) for this data set.
#### Five-Number Summary
A five-number summary consists of:
- **Minimum**: The smallest value in the data set.
- **Lower Quartile (Q1)**: The median of the lower half of the data set (25th percentile).
- **Median (Q2)**: The middle value of the data set (50th percentile).
- **Upper Quartile (Q3)**: The median of the upper half of the data set (75th percentile).
- **Maximum**: The largest value in the data set.
#### Interquartile Range (IQR)
The IQR is calculated as the difference between the upper quartile and the lower quartile. It measures the range of the middle 50% of the data.
### Summary Table
The table below is provided for filling in the five-number summary and calculating the interquartile range:
| Five-number Summary | |
|----------------------|-----|
| Minimum | |
| Lower quartile | |
| Median | |
| Upper quartile | |
| Maximum | |
| Interquartile range | |
#### Instructional Features
- **Explanation Button**: Clicking this will provide more detailed instructions and clarification on how to determine each component of the five-number summary.
- **Check Button**: After calculating the values, use this to verify your answers.
This interactive approach aids in comprehending statistical summaries and promotes hands-on learning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ee5d418-4908-4b12-8875-38434e326383%2F764077b4-451b-4f78-8967-4c59238fcb57%2F7lwvfk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Ages of Music Teachers Analysis
The following data set represents the ages of 12 music teachers in a school district:
\[ 31, 33, 36, 38, 39, 40, 40, 42, 43, 50, 52, 56 \]
These ages are arranged in ascending order. The task is to determine the five-number summary and the interquartile range (IQR) for this data set.
#### Five-Number Summary
A five-number summary consists of:
- **Minimum**: The smallest value in the data set.
- **Lower Quartile (Q1)**: The median of the lower half of the data set (25th percentile).
- **Median (Q2)**: The middle value of the data set (50th percentile).
- **Upper Quartile (Q3)**: The median of the upper half of the data set (75th percentile).
- **Maximum**: The largest value in the data set.
#### Interquartile Range (IQR)
The IQR is calculated as the difference between the upper quartile and the lower quartile. It measures the range of the middle 50% of the data.
### Summary Table
The table below is provided for filling in the five-number summary and calculating the interquartile range:
| Five-number Summary | |
|----------------------|-----|
| Minimum | |
| Lower quartile | |
| Median | |
| Upper quartile | |
| Maximum | |
| Interquartile range | |
#### Instructional Features
- **Explanation Button**: Clicking this will provide more detailed instructions and clarification on how to determine each component of the five-number summary.
- **Check Button**: After calculating the values, use this to verify your answers.
This interactive approach aids in comprehending statistical summaries and promotes hands-on learning.
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