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