2.2.3. Histogram

The term histogram was introduced by Pearson (1895) and defined as "...a term for a common form of graphical representation, i.e., by columns marking as areas the frequency corresponding to the range of their base" (p. 399).

Figure 12 shows an example of a histogram.


Figure 12. Example of a histogram.

The area of a rectangle is the width x height, which should equal the (absolute) frequency and since the width is determined by the class width, we obtain the following equation: Class Width x Height = (Absolute) Frequency. From this we can deduce that Height = Absolute Frequency / Class Width, which is the same formula for the Frequency Density. Therefore the height of the bars in a histogram is determined by the frequency density and NOT the absolute frequency itself (which is represented by the area of the bar).

Note that many books and software programs do use the absolute frequency as the height in a histogram. When all classes have the same width this is not a big problem, but when they vary it is misleading.

Bar-charts and histograms are often incorrectly considered to be the same. An overview of the main differences is summarized in Table 9.

Table 9
Differences between Bar-charts and Histograms

	Bar-chart	Histogram
Type of data	Discrete	Continuous
Width of the bars / bins	Freely to choose, but all bars the same width	Depends on the class width
Height of the bars / bins	Any type of frequency	Any type of frequency density
Positioning of bars / bins	Small gaps between the bars to highlight the discrete data type	No gaps

 

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References
Pearson, K. (1895). Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material. Philosophical Transactions of the Royal Society of London. (A.), 186, 343–414. doi:10.1098/rsta.1895.0010