Frequency Plots: histogram, bar chart and dot plot

Overview

A frequency plot is a graph that shows the pattern in a set of data by plotting how often particular values of a measure occur.

How to use it

Frequency plots are useful to investigate the spread of continuous data and whether it clusters or forms a particular shape (for example the familiar normal (bell-shaped) curve, or alternatively has two peaks).

The horizontal axis of a frequency plot graph shows groupings (say age bands of 0-5, 6 to 10, 11 to 15 etc) of a continuous measure (e.g. age, time, weight, temperature) while the vertical axis shows the number of times that a value in that group was seen.

If a graph uses vertical bars for each grouping of a continuous measure it is described as a histogram. We only use the term histogram when plotting continuous data (measured using an interval scale) or activity data. It does not make sense to rearrange the bars of a histogram because they represent groupings on a continuous scale.

For mutually-exclusive categories we use a closely-related graph – a bar chart. Similar to a histogram, the categories (rather than groupings of a continuous measure) are marked along the horizontal axis, and how often an event in that category occurs determines the height of the bar. On a bar chart the order of the vertical bars can be rearranged because each is an independent category.

When the categories are ordered by frequency the bar chart is called a Pareto chart. Pareto charts are particularly useful in determining where to concentrate improvement efforts (see separate tool page).

If a graph uses dots to show each observation within a grouping or category then it is described as a dot plot.  Dot plots can be used in place of both histograms and bar charts.  Dot plots are most suitable for situations where there are only a few options on the horizontal axis and not too many occurrences of each grouping or option.

Example of a Histogram

Example of a Dot Plot

Frequency plots should generally be constructed using thirty or more data points. They can be misleading, however, if values from stable (only random variation observed) and unstable (showing non-random or special cause variation) phases of a process are brought together. It is therefore useful to construct a time-series (runor control chart) first.

Separate frequency plots for time periods with a stable process and where the process is unstable can then be produced. This can be very helpful in understanding what might be going on differently between the two phases.

If there are obvious stratifiers (factors we already know cause differences in care processes or outcomes; for example, day v night or week v week-end) it is good to separate the contributions when plotting. You could use different colours in a stacked bar (or different symbols in a dotplot). Alternatively side-by-side separate graphs (with same scale on axes) can be easier to understand.

What next?

Detailed instructions on how to construct a histogram  are available at the IHI website. In Excel both histograms and bar charts can be drawn using the column chart type of graph. Making dot plots in Excel is not very straightforward but this tutorial  shows how it can be done. More details on Pareto charts are available here (as a separate tool).