# How to Create a Box-Plot Chart

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A box-plot chart is used to represent the distribution of data. Box plots are commonly used to highlight outlying data, such as outstanding or subpar test scores. Box-plot charts are one dimensional and can be drawn vertically or horizontally. To draw a box plot chart, you need to know the quartiles of the data, the median and any outliers.

Determine the median value of the data set by finding the value in the middle of the data set. If there are an even number of data points, use the average of the two middle values. For example, if you have the data set {8, 10, 12, 14, 16, 18, 24}, the median value would be 14.

Determine the upper quartile value by taking the middle number of the data points above the number used as the median. For example, if you have the data set {8, 10, 12, 14, 16, 18, 35}, the upper quartile would be 18.

Determine the lower quartile value by taking the middle number of the data points below the number used as the median. For example, if you have the data set {8, 10, 12, 14, 16, 18, 35}, the lower quartile would be 10.

Draw a box that has a lower end at the lower quartile value and the upper end at the upper quartile value. The width of the box is insignificant. For example, you would draw a box that started at 10 and ended at 18.

Draw a line across the box at the median value. For example, you would draw a line inside the box at 14.

Determine the inner quartile range (IQR) by subtracting the lower quartile value from step 3 from the upper quartile value from step 2. For example, you would subtract 18 from 10 to find the IQR equals 8.

Determine whether the difference between the maximum value and the upper quartile is greater than 1.5 times the IRQ. Draw a line upwards from the box as long as the lesser value. For example, since the difference between 18 and 35 (17) is greater than 1.5 times the IQR (12), you would draw a line 12 units long extending up from the box.

Determine whether the difference between the minimum value and the lower quartile is greater than 1.5 times the IRQ. Draw a line downwards from the box as long as the lesser value. For example, since the difference between 10 and 8 (2) is less than 1.5 times the IQR (12), you would draw a line 2 units long extending down from the box.

Mark an asterisk for any values that fall outside the lines draw upwards and downward from the box. For example, since 35 is outside the line extending upwards, you would mark an asterisk at 35. However, there would be no asterisk below the box because the line goes to the minimum value.

#### Things You'll Need

• Calculator
• Graph paper