Histogram

A histogram is a pictorial representation of the information in a frequency distribution or a relative frequency distribution of a data set. Histograms are used to display information about continuous variables and typically require grouping data into classes; this feature distinguishes it from a bar graph, which is primarily used for categorical or discrete data with a limited number of categories that do not require further grouping. A histogram displays the overall pattern and deviation of the data, but due to the necessity of grouping data into classes, it is not an exact representation of the data values.

Histograms are most often created using computer software but may also be created manually. To make a histogram of a data set, proceed as follows:

• 1.
  Divide the range of the data into classes of equal width.
• 2.
  Count the number of observations in each class. These counts are called frequencies, and a table of frequencies for all classes is a frequency table.
• 3.
  Draw the histogram. The width or base of the bar represents the class, and the bar height is the class frequency. The graph is drawn with no horizontal space between the bars (unless a class is empty, so that its bar has zero height).

Example

Table 1 gives the survival times in days of 72 guinea pigs after they were injected with tubercle bacilli in a medical experiment. Figure 1 is a histogram for the same data.

This histogram is skewed to the right; that is, the right side of the histogram contains the larger half of the observations in the data and extends a greater distance than the left side. A histogram is skewed to the left when its left side extends a much larger distance than the right side; a histogram is symmetric if the right and left sides have essentially the same shape. A histogram with one major peak is described as unimodal; when a histogram has two major peaks, it is described as bimodal. If every interval has essentially the same number of observations, the histogram is described as a uniform histogram.

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Table 1 Survival Times in Days of 72 Guinea Pigs After They Were Injected With Tubercle Bacilli
45	45	53	56	56	57	58	66	67	73
74	79	80	80	81	81	81	82	83	83
84	88	89	91	91	92	92	97	99	99
100	100	101	102	102	102	103	104	107	108
109	113	114	118	121	123	126	128	137	138
139	144	145	147	156	162	174	178	179	184
191	198	211	214	243	249	329	380	403	511
522	598
Source: Adapted from Bjerkedal (1960).

Figure 1 Survival Times in Days of 72 Guinea Pigs After They Were Injected With Tubercle Bacilli

Source: Adapted from Bjerkedal (1960).

Note that the selection of the number of bars to be included, which may also be stated as selection of the width of the bars, is an important decision. The same data displayed in histograms using varying bar widths can appear quite different, a fact that may be explored using Azzalini and Bowman's data and West and Ogden's histogram applet cited below.