# Class interval

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Definition
 Class Interval The individual groups of scores used in a grouped frequency distribution. Used in the creation of histograms. Also called bin width.

Tip: Some "rules of thumb" for estimating the number of class intervals for a dataset[1]...
• Sturgis's Rule: Set the number of class intervals as close as possible to , where  is the base  logarithm of the number of observations, n. The formula can also be written as  where  is the base  logarithm of the number of observations. According to Sturgis' rule,  observations would be graphed with  class intervals since  is the closest integer to .
• Rice Rule: Set the number of class intervals to twice the cube root of the number of observations. In the case of  observations, the Rice rule yields  class intervals (compared to the  recommended by Sturgis' rule).
• Experiment with different choices of width, choosing an interval width according to how well it communicates the shape of the distribution when displayed as a histogram.

## Examples

Pulse rates, in beats per minute, were calculated for  students enrolled in a statistics course at the University of Adelaide.[2] The pulse rates in the dataset range from  to  beats per minute,  possible values. An ungrouped frequency distribution listing the counts for each of the  possible values will be large and cumbersome to interpret effectively. Interpretation is simplified by grouping the data into class intervals.

Use the number of observations, in this example , to determine the number of class intervals to use in a grouped frequency distribution:

• Sturgis's rule, , suggests  or  class intervals.
• The Rice rule, , suggests  or  class intervals.

There is no right answer for the number of class intervals. For this example we will group the data into  classes, splitting the difference between the two methods.

The following frequency table provides the count and percent for the data values grouped into  class intervals.

Pulse Rate for a Sample of Students
Pulse Rate* Count Percent
(34-41] 2 1.0%
(41-48] 2 1.0%
(48-55] 4 2.1%
(55-62] 19 9.9%
(62-69] 40 20.8%
(69-76] 53 27.6%
(76-83] 30 15.6%
(83-90] 27 14.1%
(90-97] 10 5.2%
(97-104] 5 2.6%
Total 192 100.0%
• The limits of each class are indicated by the parenthesis, which means
"not including", and the square bracket, which means "including".

# Web Resources

 Write here links for external definitions

## Notes

1. "Histograms" in Chapter: 2. Graphing Distributions. Online Statistics: An Interactive Multimedia Course of Study. Retrieved on 2009-02-12.
2. See the dataset, survey, available in the MASS package in R, an open source statistical computing software application.