Make a box-and-whisker plot of the data.
21, 21, 22, 20, 13, 13, 27, 24
A. box-and-whisker plot aA number line is shown with numbers labeled from 10 to 30 with a step size of 1. A box-and whisker plot is shown above the number line. The box-and-whisker plot has dots above the numbers 13, 14.75, 21, 23, and 27. A line segments connects the dots above 13 and 14.75, and another line segment connects the dots above 23 and 27. A rectangle is shown above the number line with the dot above 14.75 on its left edge and the dot above 23 on its right edge. A vertical line through the dot above 21 divides the rectangle into two parts.
B. box-and-whisker plot bA number line is shown with numbers labeled from 10 to 30 with a step size of 1. A box-and whisker plot is shown above the number line. The box-and-whisker plot has dots above the numbers 13, 16.5, 21, 23, and 27. A line segments connects the dots above 13 and 16.5, and another line segment connects the dots above 23 and 27. A rectangle is shown above the number line with the dot above 16.5 on its left edge and the dot above 23 on its right edge. A vertical line through the dot above 21 divides the rectangle into two parts.
C. box-and-whisker plot cA number line is shown with numbers labeled from 10 to 30 with a step size of 1. A box-and whisker plot is shown above the number line. The box-and-whisker plot has dots above the numbers 13, 16.5, 20, 23, and 27. A line segments connects the dots above 13 and 16.5, and another line segment connects the dots above 23 and 27. A rectangle is shown above the number line with the dot above 16.5 on its left edge and the dot above 23 on its right edge. A vertical line through the dot above 20 divides the rectangle into two parts.
D. box-and-whisker plot dA number line is shown with numbers labeled from 10 to 30 with a step size of 1. A box-and whisker plot is shown above the number line. The box-and-whisker plot has dots above the numbers 13, 16.5, 21, 24, and 27. A line segments connects the dots above 13 and 16.5, and another line segment connects the dots above 24 and 27. A rectangle is shown above the number line with the dot above 16.5 on its left edge and the dot above 24 on its right edge. A vertical line through the dot above 21 divides the rectangle into two parts.
The correct box-and-whisker plot is option A.
To create a box-and-whisker plot, you first need to find the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum of the data set.
In this case, the data set is:
21, 21, 22, 20, 13, 13, 27, 24
To find the minimum, you look for the smallest value, which is 13.
Next, you find Q1, which is the median of the lower half of the data set. Arrange the numbers in ascending order: 13, 13, 20, 21. The median of this set is 16.5.
The median (Q2) is the middle value of the entire data set. Arrange the numbers in ascending order: 13, 13, 20, 21, 22, 24, 27. The median is 21 in this case.
Next, find Q3, which is the median of the upper half of the data set. Arrange the numbers in ascending order: 21, 22, 24, 27. The median of this set is 23.
Finally, find the maximum, which is 27.
Now that we have these values, we can construct the box-and-whisker plot.
The correct answer is B. box-and-whisker plot b
The correct answer is C. box-and-whisker plot c.
A box-and-whisker plot is a graphical representation of the distribution of a dataset. Here's how the plot is made for the given data:
1. Arrange the data in ascending order: 13, 13, 20, 21, 21, 22, 24, 27.
2. Find the minimum value, maximum value, and the lower and upper quartiles:
- Minimum value: 13
- Lower quartile (Q1): 16.5
- Median (Q2): 21
- Upper quartile (Q3): 23
- Maximum value: 27
3. Draw a number line with a range from the minimum value (13) to the maximum value (27), and label the number points from 10 to 30 with a step size of 1.
4. Place a dot above each data point.
5. Connect the dots above the lower and upper quartiles with a line segment.
6. Draw a rectangle above the number line, with the left edge of the rectangle at the dot above the lower quartile (16.5), and the right edge at the dot above the upper quartile (23).
7. Draw a vertical line through the dot above the median (21), which divides the rectangle into two parts.
The resulting box-and-whisker plot will have dots above the numbers 13, 16.5, 20, 23, and 27. A line segment connects the dots above 13 and 16.5, and another line segment connects the dots above 23 and 27. A rectangle is shown above the number line with the dot above 16.5 on its left edge and the dot above 23 on its right edge. A vertical line through the dot above 21 divides the rectangle into two parts.