 # Histograms and histographs

## Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please contact us to request a format other than those available.

The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form. A histogram divides up the range of possible values in a data set into classes or groups. For each group, a rectangle is constructed with a base length equal to the range of values in that specific group, and an area proportional to the number of observations falling into that group. This means that the rectangles will be drawn of non-uniform height. A histogram has an appearance similar to a vertical bar graph, but when the variables are continuous, there are no gaps between the bars. When the variables are discrete, however, gaps should be left between the bars. Figure 1 is a good example of a histogram. A vertical bar graph and a histogram differ in these ways:

• In a histogram, frequency is measured by the area of the column.
• In a vertical bar graph, frequency is measured by the height of the bar.

## Histogram characteristics

Generally, a histogram will have bars of equal width, although this is not the case when class intervals vary in size. Choosing the appropriate width of the bars for a histogram is very important. As you can see in the example above, the histogram consists simply of a set of vertical bars. Values of the variable being studied are measured on an arithmetic scale along the horizontal x-axis. The bars are of equal width and correspond to the equal class intervals, while the height of each bar corresponds to the frequency of the class it represents.

The histogram is used for variables whose values are numerical and measured on an interval scale. It is generally used when dealing with large data sets (greater than 100 observations). A histogram can also help detect any unusual observations (outliers) or any gaps in the data.

## Histographs

A histograph, or frequency polygon, is a graph formed by joining the midpoints of histogram column tops. These graphs are used only when depicting data from the continuous variables shown on a histogram.

A histograph smoothes out the abrupt changes that may appear in a histogram, and is useful for demonstrating continuity of the variable being studied. Figure 2 and 3 are good examples of histographs.  Unlike Figure 2, this histograph has spaces between the bars. By just looking at this illustration, the reader can immediately tell that the spaces mean the variables are discrete. In this way, histographs make it easier for the readers to determine what type of variables has been used.