# 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 $1 + log_{2}n\,$, where $log_{2}n\,$ is the base $2$ logarithm of the number of observations, n. The formula can also be written as $1 + 3.3\,log_{10}n\,$ where $log_{10}n\,$ is the base $10$ logarithm of the number of observations. According to Sturgis' rule, $1000$ observations would be graphed with $11$ class intervals since $10$ is the closest integer to $log_{2}1000\,$.
• Rice Rule: Set the number of class intervals to twice the cube root of the number of observations. In the case of $1000$ observations, the Rice rule yields $20$ class intervals (compared to the $11$ 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 $192$ students enrolled in a statistics course at the University of Adelaide.[2] The pulse rates in the dataset range from $35$ to $104$ beats per minute, $70$ possible values. An ungrouped frequency distribution listing the counts for each of the $70$ 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 $n=192\,$, to determine the number of class intervals to use in a grouped frequency distribution:

• Sturgis's rule, $1 + 3.3\,log_{10}192=8.6\,$, suggests $8$ or $9$ class intervals.
• The Rice rule, $2 \times \sqrt[3]{192}=11.54$, suggests $11$ or $12$ class intervals.

There is no right answer for the number of class intervals. For this example we will group the data into $10$ classes, splitting the difference between the two methods.

The following frequency table provides the count and percent for the data values grouped into $10$ 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.