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- 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.
Pulse rates, in beats per minute, were calculated for $ $ students enrolled in a statistics course at the University of Adelaide. 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.
- The limits of each class are indicated by the parenthesis, which means
"not including", and the square bracket, which means "including".
- "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.