Question
Calculate the 5-number summary of the skewed dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29. When constructing the box plot on a number line, which explains a reason why the dataset is skewed?(1 point)
Responses
The median is exactly in the middle of the box.
The median is exactly in the middle of the box.
The 5 numbers in the summary are equally spread apart.
The 5 numbers in the summary are equally spread apart.
The whiskers are the same length.
The whiskers are the same length.
The right whisker is much longer than the left whisker.
Responses
The median is exactly in the middle of the box.
The median is exactly in the middle of the box.
The 5 numbers in the summary are equally spread apart.
The 5 numbers in the summary are equally spread apart.
The whiskers are the same length.
The whiskers are the same length.
The right whisker is much longer than the left whisker.
Answers
Answered by
GPT-4o mini
To calculate the 5-number summary of the dataset \(15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29\), we need to identify the following:
1. **Minimum**: The smallest number in the dataset, which is \(15\).
2. **First Quartile (Q1)**: The median of the first half of the data. The first half is \(15, 16, 16, 17, 17\). The median of this subset is \(16\).
3. **Median (Q2)**: The median of the entire dataset. Since there are 11 numbers, the median is the sixth number, which is \(18\).
4. **Third Quartile (Q3)**: The median of the second half of the data. The second half is \(18, 18, 19, 19, 29\). The median of this subset is \(19\).
5. **Maximum**: The largest number in the dataset, which is \(29\).
Now, we summarize these values as follows:
- Minimum: \(15\)
- First Quartile (Q1): \(16\)
- Median (Q2): \(18\)
- Third Quartile (Q3): \(19\)
- Maximum: \(29\)
Thus, the 5-number summary is:
- **Minimum**: 15
- **Q1**: 16
- **Median (Q2)**: 18
- **Q3**: 19
- **Maximum**: 29
### Analysis of Skewness
To determine why the dataset is considered skewed, we can assess the position and lengths of the whiskers in a box plot representing this data.
When constructing the box plot, we would note that:
- The whisker on the right (from Q3 to the maximum, which is 29) is longer than the whisker on the left (from Q1 to the minimum, which is 15).
In summary, the correct response that explains why the dataset is skewed is:
**The right whisker is much longer than the left whisker.**
1. **Minimum**: The smallest number in the dataset, which is \(15\).
2. **First Quartile (Q1)**: The median of the first half of the data. The first half is \(15, 16, 16, 17, 17\). The median of this subset is \(16\).
3. **Median (Q2)**: The median of the entire dataset. Since there are 11 numbers, the median is the sixth number, which is \(18\).
4. **Third Quartile (Q3)**: The median of the second half of the data. The second half is \(18, 18, 19, 19, 29\). The median of this subset is \(19\).
5. **Maximum**: The largest number in the dataset, which is \(29\).
Now, we summarize these values as follows:
- Minimum: \(15\)
- First Quartile (Q1): \(16\)
- Median (Q2): \(18\)
- Third Quartile (Q3): \(19\)
- Maximum: \(29\)
Thus, the 5-number summary is:
- **Minimum**: 15
- **Q1**: 16
- **Median (Q2)**: 18
- **Q3**: 19
- **Maximum**: 29
### Analysis of Skewness
To determine why the dataset is considered skewed, we can assess the position and lengths of the whiskers in a box plot representing this data.
When constructing the box plot, we would note that:
- The whisker on the right (from Q3 to the maximum, which is 29) is longer than the whisker on the left (from Q1 to the minimum, which is 15).
In summary, the correct response that explains why the dataset is skewed is:
**The right whisker is much longer than the left whisker.**
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