Class interval

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Definition

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 , where is the base 2 logarithm of the number of observations, n. The formula can also be written as where 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 .
  • 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 , to determine the number of class intervals to use in a grouped frequency distribution:

  • Sturgis's rule, , suggests 8 or 9 class intervals.
  • The Rice rule, , 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
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".



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.
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