Math and Statistics Homework Help Free Math & Statistics Homework Help

Grouped Frequency Distributions

To construct a grouped frequency distribution, the data are sorted and separated into groups called classes.  Usually 5 to 20 classes are used, but in any case, make sure that you use enough classes to give a good description of the data.  The number (frequency) of data belonging to each class is then recorded in a table of frequencies called a frequency table.  This table describes the distribution of frequencies.

There are 5 rules for the classes in a grouped frequency distribution.

1.  The classes must be mutually exclusive (non-overlapping).  This means that there is no way that any of the data could fall into 2 different classes at once.

2.  The classes must be continuous.  This means that there can be no gaps in the classes.  Even if there are no values in a particular class, you cannot omit that class unless it is the first or last class (in which case it should not have been included in the first place).

3.  The classes must be exhaustive.  This means that there must be a class for every data value in the data set so that every data value is included in the frequency distribution.

4.  The classes must be of equal width, otherwise the frequency distribution would give a distorted view of the data.  The class width is found by either subtracting the upper (or lower) class limit of one class from the upper (or lower) limit of the next class or by subtracting the upper boundary from the lower boundary of any given class.  Note that an exception is made for open ended distributions that have no specific beginning or ending value.  An example of the class limits for two such open-ended distributions are below.

 Age Time 0 - 9 Below 100 10 - 19 101 - 110 20 - 29 111 - 120 30 - 39 121 - 130 40 - 49 131 - 140 50 and older 141 - 140

5.  The class width should be an odd number so that the class midpoints have the same place value as the data.

Example: Suppose our data set is {1, 2, 3, 2, 1, 3, 2, 4, 2, 1, 0 ,1, 3, 2, 4, 2, 1, 2, 1, 1}.  If you cut & paste that data into the data sorter below and you get 0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,4,4.

 Enter Data Separated By Commas: The Sorted Data Are:

These data would fit nicely into five classes of width one.

The frequency table is below.

 Classes (Limits) Class Boundaries Frequencies 0 -0.5 - 0.5 1 1 0.5 - 1.5 7 2 1.5 - 2.5 7 3 2.5 - 3.5 3 4 3.5 - 4.5 2