A box and whisker plot is used to show the distribution of a data set.^{[2]} Each quartile is marked on the graph, and a box is drawn to represent the 2^{nd} and 3^{rd} quartiles. Lines are drawn to represent the 1^{st} and 4^{th} quartiles. These are the 'whiskers'. The box and whisker plot in figure 1 represents the data set { 2, 2, 3, 4, 5, 5, 6, 7, 8, 9 }.
Figure 1: Box and Whisker Plot |
A box and whisker plot is also called a box plot or a boxplot.
For this example, use the data set { 1, 8, 4, 3, 9, 3, 6, 4, 7 }.
Step | Description | Example |
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1 | Draw a number line that will contain the box and whisker plot. | |
2 | Determine the median of the data set. The median of this data set is 4. Draw a vertical line under the 4. | |
3 | Now calculate the start of the 1^{st} quartile. Take the first half of the data set: { 1, 3, 3, 4 }. Find the median of the first half of the data set. In this case, the median is 3 + 3 = 6. 6 / 2 = 3. Make a line under the 3. | |
4 | Complete the box for the 2^{nd} quartile. | |
5 | Calculate the start of the 4^{th} quartile. Take the second half of the data set: { 6, 7, 8, 9 }. Find the median of the second half of the data set. In this case, the median is 7 + 8 = 15. 15 / 2 = 7.5. Make a line under 7.5. | |
6 | Complete the box for the 3^{rd} quartile. | |
7 | Now draw a point to show the start of the 1^{st} quartile. Do not include any outliers. | |
8 | Connect the point to the middle of the 2^{nd} quartile line. | |
9 | Now draw a point to show the end of the 4^{th} quartile. Do not include any outliers. | |
10 | Connect the point to the middle of the 3^{rd} quartile line. Your box and whisker plot is now complete. |
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E | F | G | H | I |
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O | P | Q | R | S |
T | U | V | W | X |
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