UNIMODAL and BIMODAL APPLICATIONS

A unimodal data set has one mode — meaning one value appears most often.
It has one clear “peak” when you draw it on a graph.

Example:
Test scores: 4, 5, 5, 6, 7, 8

• The number 5 appears most often. This data is unimodal because it has one mode (5).

A bimodal data set has two modes — meaning two values appear most often.
It has two peaks on a graph.

Example:
Test scores: 4, 5, 5, 7, 7, 8

• The numbers 5 and 7 appear most often.  This data is bimodal because it has two modes (5 and 7).

We can characterise the shape of a data set by looking at its histogram.

First, if the data values seem to pile up into a single "mound", we say the distribution is unimodal. If there appear to be two "mounds", we say the distribution is bimodal. If there are more than two "mounds", we say the distribution is multimodal.

Second, we focus on whether the distribution is symmetric, or if it has a longer "tail" on one side or another. In the case where there is a longer "tail", we say the distribution is skewed in the direction of the longer tail. In the case where the longer tail is associated with larger data values, we say the distribution is skewed right or (positively skewed). In the case where the longer tail is associated with smaller (or more negative) values, we say the distribution is skewed left or (negatively skewed).

If the distribution is symmetric, we will often need to check if it is roughly bell-shaped, or has a different shape. In the case of a distribution where each rectangle is roughly the same height, we say we have a uniform distribution.

The below graphic gives a few examples of the aforementioned distribution shapes.

MEASURES OF SPREAD - LETS GO DEEPER

In addition to knowing where the centre is for a given distribution, we often want to know how "spread out" the distribution is -- this gives us a measure of the variability of values taken from this distribution. The graphic below shows the general shape of three symmetric unimodal distributions with identical measures of centre, but very different amounts of "spread".