Question
Problem
The data below represents the number of strikes each Sam's Inc. employee got on the company bowling outing.
\[1\],
\[3\],
\[6\],
\[8\],
\[10\],
\[12\],
\[13\],
\[13\],
\[16\],
\[18\],
\[19\]
Which box plot correctly summarizes the data?
Choose 1 answer:
Choose 1 answer:
(Choice A) A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 8. The box extends from 8 to 16 and is divided into 2 parts by a vertical line segment at 13. The right whisker extends from 16 to 19. All values estimated.
A
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 8. The box extends from 8 to 16 and is divided into 2 parts by a vertical line segment at 13. The right whisker extends from 16 to 19. All values estimated.
(Choice B) A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
B
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
(Choice C) A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 8. The box extends from 8 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
C
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 8. The box extends from 8 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
Related content
Answers
GPT-4o mini
To determine the correct box plot that summarizes the data, we first need to calculate the required quartiles and key statistics:
The data provided is:
\[1, 3, 6, 8, 10, 12, 13, 13, 16, 18, 19\]
1. **Order the data**: The data is already sorted in ascending order.
2. **Determine the minimum and maximum**:
- Minimum = \(1\)
- Maximum = \(19\)
3. **Calculate the median (Q2)**:
- There are 11 data points (odd number), so the median is the 6th value.
- Median (Q2) = \(12\)
4. **Calculate the first quartile (Q1)**:
- The first quartile is the median of the first half of the data, which consists of \(1, 3, 6, 8, 10\). The median of these five values (the 3rd value) is \(6\).
- Q1 = \(6\)
5. **Calculate the third quartile (Q3)**:
- The third quartile is the median of the second half of the data, which consists of \(12, 13, 13, 16, 18, 19\).
- The median of \(12, 13, 13, 16, 18, 19\) (the average of the 3rd and 4th elements) is \((13 + 16)/2 = 14.5\).
- Q3 = \(14.5\)
6. **Construct the box plot boundaries**:
- Whiskers extend from the minimum to Q1 and from Q3 to the maximum.
- Minimum = \(1\), Q1 = \(6\), Median (Q2) = \(12\), Q3 = \(14.5\), Maximum = \(19\).
Now we can summarize:
- Lower whisker goes from \(1\) to \(6\).
- The box extends from \(6\) to \(14.5\) with a line at \(12\) for the median.
- Upper whisker goes from \(14.5\) to \(19\).
Now we can consider the choices:
- **Choice A** describes a box extending from \(8\) to \(16\), which is incorrect.
- **Choice B** describes a box from \(6\) to \(16\) and a median at \(12\), which is not correct as the upper bound of the box should be \(14.5\).
- **Choice C** describes a box from \(8\) to \(16\) with a median at \(12\), which is incorrect as the lower bound of the box should be \(6\).
Let's analyze the best match:
- **Choice B** is the closest as it has the lower whisker extending from \(1\) to \(6\) and the median at \(12\) but extends to \(16\) incorrectly.
None of the descriptions seem to perfectly match the calculated box plot. It looks like all options have inaccuracies. But of the options provided, **Choice B** correctly represents the whisker and median, so it is the best option available.
The data provided is:
\[1, 3, 6, 8, 10, 12, 13, 13, 16, 18, 19\]
1. **Order the data**: The data is already sorted in ascending order.
2. **Determine the minimum and maximum**:
- Minimum = \(1\)
- Maximum = \(19\)
3. **Calculate the median (Q2)**:
- There are 11 data points (odd number), so the median is the 6th value.
- Median (Q2) = \(12\)
4. **Calculate the first quartile (Q1)**:
- The first quartile is the median of the first half of the data, which consists of \(1, 3, 6, 8, 10\). The median of these five values (the 3rd value) is \(6\).
- Q1 = \(6\)
5. **Calculate the third quartile (Q3)**:
- The third quartile is the median of the second half of the data, which consists of \(12, 13, 13, 16, 18, 19\).
- The median of \(12, 13, 13, 16, 18, 19\) (the average of the 3rd and 4th elements) is \((13 + 16)/2 = 14.5\).
- Q3 = \(14.5\)
6. **Construct the box plot boundaries**:
- Whiskers extend from the minimum to Q1 and from Q3 to the maximum.
- Minimum = \(1\), Q1 = \(6\), Median (Q2) = \(12\), Q3 = \(14.5\), Maximum = \(19\).
Now we can summarize:
- Lower whisker goes from \(1\) to \(6\).
- The box extends from \(6\) to \(14.5\) with a line at \(12\) for the median.
- Upper whisker goes from \(14.5\) to \(19\).
Now we can consider the choices:
- **Choice A** describes a box extending from \(8\) to \(16\), which is incorrect.
- **Choice B** describes a box from \(6\) to \(16\) and a median at \(12\), which is not correct as the upper bound of the box should be \(14.5\).
- **Choice C** describes a box from \(8\) to \(16\) with a median at \(12\), which is incorrect as the lower bound of the box should be \(6\).
Let's analyze the best match:
- **Choice B** is the closest as it has the lower whisker extending from \(1\) to \(6\) and the median at \(12\) but extends to \(16\) incorrectly.
None of the descriptions seem to perfectly match the calculated box plot. It looks like all options have inaccuracies. But of the options provided, **Choice B** correctly represents the whisker and median, so it is the best option available.