Question
Which box plot represents a set of data that has the greatest mean absolute deviation?
A box-and-whisker plot. The whiskers have a range of 5 units, and the box has a range of 3.5 units.
A box-and-whisker plot. The whiskers have a range of 9 units, and the box has a range of 7 units.
A box-and-whisker plot. The whiskers have a range of 6 units, and the box has a range of 3 units.
A box-and-whisker plot. The whiskers have a range of 4.5 units, and the box has a range of 2 units.
A box-and-whisker plot. The whiskers have a range of 5 units, and the box has a range of 3.5 units.
A box-and-whisker plot. The whiskers have a range of 9 units, and the box has a range of 7 units.
A box-and-whisker plot. The whiskers have a range of 6 units, and the box has a range of 3 units.
A box-and-whisker plot. The whiskers have a range of 4.5 units, and the box has a range of 2 units.
Answers
Answered by
GPT-4o mini
Mean absolute deviation (MAD) is a measure of the dispersion of a dataset. A larger MAD indicates that the data points are, on average, farther from the mean, suggesting greater variability.
While box plots typically display the spread of data through the interquartile range (IQR) and outliers, we can get an insight into possible MAD values through the ranges provided in your options.
Let's analyze the box-and-whisker plots you've described:
1. **First Box Plot**:
- Whiskers: 5 units
- Box: 3.5 units
- Total range (max-min): 5 + 3.5 = 8.5 units
2. **Second Box Plot**:
- Whiskers: 9 units
- Box: 7 units
- Total range: 9 + 7 = 16 units
3. **Third Box Plot**:
- Whiskers: 6 units
- Box: 3 units
- Total range: 6 + 3 = 9 units
4. **Fourth Box Plot**:
- Whiskers: 4.5 units
- Box: 2 units
- Total range: 4.5 + 2 = 6.5 units
The second box plot has the largest total range (16 units), which suggests that it has the greatest dispersion and thus is likely to have the highest mean absolute deviation.
Therefore, the box plot that represents a set of data that has the greatest mean absolute deviation is:
**The second box-and-whisker plot. The whiskers have a range of 9 units, and the box has a range of 7 units.**
While box plots typically display the spread of data through the interquartile range (IQR) and outliers, we can get an insight into possible MAD values through the ranges provided in your options.
Let's analyze the box-and-whisker plots you've described:
1. **First Box Plot**:
- Whiskers: 5 units
- Box: 3.5 units
- Total range (max-min): 5 + 3.5 = 8.5 units
2. **Second Box Plot**:
- Whiskers: 9 units
- Box: 7 units
- Total range: 9 + 7 = 16 units
3. **Third Box Plot**:
- Whiskers: 6 units
- Box: 3 units
- Total range: 6 + 3 = 9 units
4. **Fourth Box Plot**:
- Whiskers: 4.5 units
- Box: 2 units
- Total range: 4.5 + 2 = 6.5 units
The second box plot has the largest total range (16 units), which suggests that it has the greatest dispersion and thus is likely to have the highest mean absolute deviation.
Therefore, the box plot that represents a set of data that has the greatest mean absolute deviation is:
**The second box-and-whisker plot. The whiskers have a range of 9 units, and the box has a range of 7 units.**