# Histogram

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Definition
 Histogram A graph consisting of a series of vertical columns, such that the area of each column represents observed frequencies in a class interval (also referred to as interval or bin). Used to display the shape of a frequency distribution. Particularly useful when there are a large number of observations. A type of bar graph. Also called histograph.

Tip: When creating a histogram...
• Leave no space between bars when the class intervals represent continuous data; bar graphs, drawn with a gap between bars, are used to represent discrete data (i.e., different categories).
• Graph the observed frequency in each class interval (also called the class frequency) for datasets with a small to medium number of observations; label the y-axis "Frequency." Graph the relative frequency in each class interval for datasets with a large number of observations; label the y-axis "Proportion" or "Relative Frequency."

## Examples

### A typical histogram

Pulse rates, in beats per minute, were calculated for 192 students enrolled in a statistics course at the University of Adelaide.[1] The first step in creating a histogram is to create a frequency table.

Pulse Rate for a Sample of Students
Pulse Rate Count
(34-41] 2
(41-48] 2
(48-55] 4
(55-62] 19
(62-69] 40
(69-76] 53
(76-83] 30
(83-90] 27
(90-97] 10
(97-104] 5
Total 192

Using the class frequencies (the number of observations in each class interval) shown in the frequency table, the following histogram was created.[2]

### Exploring the effect of class interval size

See West's histogram applet for an opportunity to experiment with different class interval sizes.

## Notes

1. See the dataset, survey, available in the MASS package in R, an open source statistical computing software application.
2. Created in R using the command:
hist(Pulse,breaks=c(34,41,48,55,62,69,76,83,90,97,104),xlab="Pulse, beats/min",main="Pulse Rate for a Sample of Students")