Class interval

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Class Interval

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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 [math]1 + log_{2}n\,[/math], where [math]log_{2}n\,[/math] is the base [math]2[/math] logarithm of the number of observations, n. The formula can also be written as [math]1 + 3.3\,log_{10}n\,[/math] where [math]log_{10}n\,[/math] is the base [math]10[/math] logarithm of the number of observations. According to Sturgis' rule, [math]1000[/math] observations would be graphed with [math]11[/math] class intervals since [math]10[/math] is the closest integer to [math]log_{2}1000\,[/math].
  • Rice Rule: Set the number of class intervals to twice the cube root of the number of observations. In the case of [math]1000[/math] observations, the Rice rule yields [math]20[/math] class intervals (compared to the [math]11[/math] 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.


Pulse rates, in beats per minute, were calculated for [math]192[/math] students enrolled in a statistics course at the University of Adelaide.[2] The pulse rates in the dataset range from [math]35[/math] to [math]104[/math] beats per minute, [math]70[/math] possible values. An ungrouped frequency distribution listing the counts for each of the [math]70[/math] 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 [math]n=192\,[/math], to determine the number of class intervals to use in a grouped frequency distribution:

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

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

The following frequency table provides the count and percent for the data values grouped into [math]10[/math] class intervals.

Pulse Rate for a Sample of Students
from the University of Adelaide
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".

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Web Resources

  • Write here links for external definitions


  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.