Histograms

by Shea Molloy

Definition

The word histogram comes from the Greek 'histos', meaning "anything that stands upright", and 'gram', which means chart or graph (source: NCSS Statistical Software, Etymology online). The term was coined by  Karl  Peterson in 1895.

Histograms are accurate representations of continuous, numerical data on a singular axis. A histogram is a visualization of the frequency distribution in which the vertical axis represents the count (frequency) and the horizontal axis represents the possible range of the data values.

The anatomy of a histogram. Source: Data Visualization Catalogue.

Each bar in a histogram represents the frequency of scores within the intervals (also known as bins). Histograms help estimate where values are concentrated, what the extremes are and whether there are any gaps or unusual values. The bins are the main differentiator from a bar chart: a histogram can only plot the frequency of score occurrences whereas a bar chart can plot many other kinds of data. Histograms can also be normalized to display relative frequencies, which will quickly show how often data occur in relation to other data. Histograms are useful for:

  • Comparing data within intervals
  • Showing data over time
  • Displaying and analyzing distribution
  • Finding patterns across ranges
An example of a simple histogram with distribution outlined. Source: OriginLab

Creation

The bars produced in histograms are used to represent the shape of the distribution of data and as such are used to perform communicate business and math analysis. Bar shapes can vary in height or width, as long as the groups are defined in a way that clearly communicates any relevant patterns. Creating a histogram can be straightforward if the data is grouped correctly. It is important to try filtering the data several times to explore relevant patterns.

A good binning method will clearly identify patterns within the data. Source: Chartio

Several methods have been developed for optimizing data bins in creating histograms. Bayesian blocks, shown below, is a dynamic histogramming method utilizing probability density functions to program bin widths.

Examples of different grouping methods for histograms. Source: AstroML.
An example of a log-scaled histogram. Source: Wolfram

Histograms don't have to remain vertical; radial histograms, polar histogram and angle histograms are useful for examining peaks and identifying abnormalities in distribution from a similar starting point.

Polar coordinates help communicate more data with clarity. Source: Yahia El Gamal

Analysis

With the right bins, analyzing a histogram can be one of the quickest ways to communicate patterns across a data set. As histograms examine frequencies rather than other kinds of data, it is easier to tell if a distribution has any irregularities  within it. Here are some examples of what different distributions might look like in a histogram and what they mean:

Normal distribution: shows that scores occur as frequently on one side of the average as the other. Source: ASQ Education
Skewed distribution: a distributions that show natural limits on one side of the average. Source: ASQ Education
Bimodal distribution: distribution that shows two variables affecting scores within one data set. Source: ASQ Education
Multimodal or Plateau distribution: a distribution showing many processes occurring within the data setSource: ASQ Education
Edge Peak distribution: similar to a normal distribution, but often with either an outlier variable or a fault in the construction of the histogram using a "greater than" function that lumps more data on one side. Source: ASQ Education
Comb distribution: often shows that the data is grouped incorrectly Source: ASQ Education

Creative Histograms

The following histograms expand on histogramming methodology to convey more data, as clearly as a classic histogram.

A simple histogram displaying frequency of judgements on /r/AmITheAsshole. Source: /r/DataisBeatiful.
  • Comprehensible bins
  • Shows an obvious pattern
A radial histogram showing the application of antibiotics after WWII. Source: borgar
  • Quickly identifies spikes in frequency
  • Well labelled
  • Clear differentiators
A cool demo for layering frequencies with alternative data. Source: Maria M on Observable.
  • Displays data within frequency
  • Uses multiple retinal variables without confusing the reader (at least n sample data)
Shows several variables within across frequency. Source: Python Graph Gallery.
  • Combines several data sets across frequency
  • Clear labeling