Box and Whisker Plot

Also Known As
Box Plot

A box and whisker plot is a graphical means of displaying the variation in a dataset. This plot provides more detail than a histogram and allows multiple sets of data to be displayed in the same graph.


When comparing multiple sets of data.

When analyzing or conveying the most significant features of a dataset, instead of the detail.

When summarizing data from another graph, for example, a control chart or run chart.

When there is insufficient data for a histogram.

How do I use this tool?

1. LIST ALL THE DATA VALUES IN ORDER from smallest to largest. The total number of values is = n. Refer to the numbers in order, where X1 is the smallest number; X2 is the next smallest number; up to Xn, which is the largest number.

2. MEDIANS. Find the median of the data. Half of the data points should be larger and half should be smaller than this point. When finding the median for an even number of data points, the median is the average of the two middle values.

3. HINGES. Divide the data into quarters. Determine the hinges, which are the medians of each half.

4. H-SPREAD. The H-spread is the calculated distance between the hinges and is equal to the upper hinge minus the lower hinge.

5. INNER FENCES. Inner fences are values of separating data that are a predictable part of the distribution from data that are outside the distribution. Inner fences are located beyond each hinge at 1½ times the H-spread, a distance called a step.
Upper inner fence = upper hinge + (1.5 x H-spread)
Lower inner fence = lower hinge - (1.5 x H-spread)

6. OUTER FENCES. Data beyond these values are far outside the distribution. They are step beyond the inner fences.
Upper outer fence = upper inner fence + (1.5 x H-spread)
Lower outer fence = lower inner fence - (1.5 x H-spread)

a. Draw one horizontal axis. Scale it appropriately for the range of data.
b. Draw a box with ends at the hinge values.
c. Draw a line across the middle of the box at the median value.
d. Draw a line at each inner fence value.
e. Draw a dashed crossbar at the adjacent value, the first value inside the inner fences.
f. Draw whiskers, dashed lines from the ends of the box to the adjacent values.
g. Draw small circles representing any outside data points: beyond the inner fences but inside the outer fences.
h. Draw double circles to represent far out data points: beyond the outer fences.
i. When comparing several datasets, repeat the procedure for each set of data.

8. ANALYZE THE PLOT. Look for:
a. Location of the median;
b. Spread of the data: how far the hinges and fences are from the median;
c. Symmetry of the distribution;
d. Existence of outside points.

Expertise Required
This tool is easy to use and requires little or no training.
Recommended Supplies/Materials

Easy to read and an effective representation of the data.


Not appropriate for conveying data with substantial randomness.

Where can I go to learn more?

American Society for Quality. Data collection and analysis tools: box and whisker plot. 2009 [cited 2009 June 23]; Available from: