## Histograms

**Histograms **provide a useful way to display data and its distribution. Students often get confused between histograms and bar charts. However, histograms and bar charts are different in a number of ways. Firstly, histograms are used to present continuous grouped data whereas bar charts are used to display ordinal, nominal or discrete data. Click here to see some examples of bar charts. Secondly, bar charts are usually used to compare data whereas a histogram shows the distribution of the data. Note that you may be required to produce or interpret histograms for a given dataset but you may also be asked to do it for a dataset that you are already familiar with. See more on this.

The most important aspect of histograms is that they are not plotted against frequency, **they are plotted against frequency density. **This means that the frequency is represented in the area of the bar.

Since the area of a rectangle is width multiplied by height, we have:

FREQUENCY = FREQUENCY DENSITY INTERVAL WIDTH

See the worked example for an application of this. Note that the area may be exactly the frequency but it is also possible to use proportional areas. In these cases:

FREQUENCY = AREA

where – see Example 1. If the interval widths are uniform, a frequency polygon (see more on Frequency Polygons) can be added to a histogram by joining up the midpoints of the top of each bar of the histogram with straight lines. See Example 1d. Histograms also provide a convenient way to look at the ‘spread’ of data (see Measures of Variation) and connect to probability distributions. See the Box Plots page (including the example) for more on this.