Please see my other Statistics articles.

## Visually Illustrating Bounds, Median, Range

Box and Whisker Plot provides a very efficient method for communicating several measurements.

To illustrate how to create a box and whisker plot, I’ll use a free website and Excel.

First, I’ll use the following link to access the free website.

Now that my data set is ready to use in creating the diagram, I will use a free Venn Diagram Maker.

https://www.meta-chart.com/venn

Using the Data tab, I’ll enter 5 simple values.

Finally, I’ll click the Display tab to display my plot.

Below is the plot generated along with my notes (gray) to illustrate the various measurements provided by a box and whiskers plot.

The box communicates displays median, with the left and right appendages (whiskers), the lower and upper bounds, as well as using those bounds to calculate the interquartile.

This simple chart communicates the following measurements:

- The vertical line dividing the box represents the median (3).
- The far-left whisker represents the lower bound (1).
- The far-right whisker represents the upper bound (5).
- The range is the upper bound (5) – lower bound (1) = 4.
- The interquartile range (IQR) is the right (upper edge) of the box (4.5) – left (lower edge) of the box (1.5) = 3.
- Each quartile (Q) represents a portion data points, with Q2-3 residing within the IQR.
- Q1: 12.5% of data points.
- Q2: 37.5% of data points.
- Q3: 37.5% of data points.

IQR (Q2-3): 75% of data points. - Q4: 12.5% of data points.

Depending on distributions, the box (IQR) and the mean also visually communicate a general distribution of data points within the IQR. In this example the data points are evenly distribution, but in most studies, the mean line will be off-center, communicating which side of the mean or Q, in which most data points reside.

Here is a summary of values provided by the plot:

Now I’ll create a similar plot using Excel.

First, Ill begin with the same data set.

Next, I’ll highlight the data set, then choose to insert the box and whisker plot.