Box-and-Whisker Plots

Box-and-Whisker Plots

Box-and-whisker plots display summary values of a data set. The plot shows the spread of a data set and can be useful when comparing two or more data sets.

How to Create a Box-and-Whisker Plot

BS00107_.wmf (1510 bytes)

Fourteen students were asked to keep track of how much time they spent on the Internet during a one-week period. The following gives the average amounts of time (in minutes) each student spent on the Internet per night. Create a box-and-whisker plot of the data.

120, 90, 95, 60, 130, 125, 85, 80, 110, 75, 150, 115, 110, 100

Creating a Box-and-Whisker Plot
What to Do	Example
1) Write the data in numerical order from smallest to largest.	1) 60, 75, 80, 85, 90, 95, 100, 110, 110, 115, 120, 125, 130, 150
2) Find the median, the lower extreme, and the upper extreme. Lower extreme – the minimum value of the data set Upper extreme – the maximum value of the data set	2) The median is 105, the lower extreme is 60, and the upper extreme is 150
3) Find the lower and upper quartiles. Lower quartile – the median of the lower half of the data set Upper quartile – the median of the upper half of the data set	3) The lower half of the data set is: 60, 75, 80, 85, 90, 95, 100. The median of this data set is 85. The lower quartile is 85. The upper half of the data set is: 110, 110, 115, 120, 125, 130, 150. The median of this data set is 120. The upper quartile is 120.
4) Graph these five summary points below a number line.	4) See number line below.
5) Draw a box from the lower quartile to the upper quartile. Draw a vertical line through the median.	5) See box below.
6) Draw line segments, or whiskers, from the box to the extremes. Make sure your graph is a Complete Graph.	6) See final plot below.

Notes:

The box (from the lower quartile to the upper quartile) makes up 50% of the data.
Each whisker (extreme to quartile) represents 25% of the data.
The median is not necessarily in the center of the box. In fact, you may not see a line to represent the median if the median is equal to one of the quartiles.
When your data set has an outlier, you should draw the Special Case of the Box-and-Whisker Graph .

Strengths of Box-and-Whisker Plots

The following is a list of some of the strengths of a box-and-whisker plot that can help you determine whether a box-and-whisker plot is a good choice for organizing your data.

The plot shows the median, quartiles, and extremes.
The plot shows the range of the data.

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