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 d
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To create a box-and-whisker plot, follow these steps:
1. Arrange the data in ascending order: 13, 13, 20, 21, 21, 22, 24, 27.
2. Find the median (middle value) of the data set. In this case, the median is 21.
3. Find the lower quartile (Q1) and the upper quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
- Lower half: 13, 13, 20
- Upper half: 22, 24, 27
- Q1 = median of lower half = 13
- Q3 = median of upper half = 24
4. Calculate the interquartile range (IQR), which is the difference between Q3 and Q1. IQR = Q3 - Q1 = 24 - 13 = 11.
5. Determine the minimum and maximum values in the data set. The minimum is 13, and the maximum is 27.
6. Construct the box-and-whisker plot using the information calculated:
- The box: Draw a box from Q1 to Q3, in this case, from 13 to 24.
- The median: Draw a vertical line inside the box at the median (21).
- Whiskers: Draw a line from the minimum (13) to the lower end of the box and a line from the maximum (27) to the upper end of the box.
Based on the steps above, the correct answer is:
C. box-and-whisker plot c
I hope this explanation helps!