Box and Whisker Plot - ASQ

# Box and Whisker Plot

A box and whisker plot is a graphical method of displaying variation in a set of data. In most cases a histogram provides a sufficient display; however, a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Some types are called box and whisker plots with outliers.

## Why Use a Box and Whisker Plot?

Box and whisker plots are very effective and easy to read. They summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.

## When to Use a Box and Whisker Plot

Use box and whisker plots when you have multiple data sets from independent sources that are related to each other in some way. Examples include test scores between schools or classrooms, data from before and after a process change, similar features on one part such as cam shaft lobes, or data from duplicate machines manufacturing the same products.

## Box and Whisker Plot Procedure

A box and whisker plot is developed from five statistics.

1. Minimum value – the smallest value in the data set
2. Second quartile – the value below which the lower 25% of the data are contained
3. Median value – the middle number in a range of numbers
4. Third quartile – the value above which the upper 25% of the data are contained
5. Maximum value – the largest value in the data set

For example, given the following 20 data points, the five required statistics are displayed.

 Number Data 1 113 Minimum: 113 2 116 3 119 4 121 5 124 2nd Quartile: 124 6 124 7 125 8 126 9 126 10 126 Median: 126.5 11 127 12 127 13 128 14 129 15 130 3rd Quartile: 130 16 130 17 131 18 132 19 133 20 136 Maximum: 136

Note that for a data set with an even number of values, the median is calculated as the average of the two middle values.

Here are the data represented in box and whisker plot format.

Left: The center represents the middle 50%, or 50th percentile of the data set and is derived using the lower and upper quartile values. The median value is displayed inside the "box." The maximum and minimum values are displayed with vertical lines ("whiskers") connecting the points to the center box.

Right: For comparison, a histogram of the data is also shown, showing the frequency of each value in the data set.

## Box and Whisker Plot Example

Suppose you wanted to compare the performance of three lathes responsible for the rough turning of a motor shaft. The design specification is 18.85 +/- 0.1 mm.

Diameter measurements from a sample of shafts taken from each roughing lathe are displayed in a box and whisker plot.

1. Lathe 1 appears to be making good parts, and is centered in the tolerance.
2. Lathe 2 appears to have excess variation, and is making shafts below the minimum diameter.
3. Lathe 3 is performing with relatively less variation than Lathe 2; however, it is centered on the lower side of the specification and is making shafts below specification.

## Create a Box and Whisker Plot

Download the box and whisker plot template. Most software packages that perform statistical analysis can create box and whisker plots.

## References

1. Juran, J. M. and Frank M. Gryna, Juran’s Quality Control Handbook, Fourth Edition, McGraw–Hill, Inc., 1988.
2. Wortman, Bill, Certified Six Sigma Black Belt Primer, Revision 13, Quality Council of Indiana.