Frequency table
Bar charts for discrete data are based on the frequencies of the different values — i.e. the number of times each value occurs in the data set.
In data sets with a small number of possible counts (say 20 or fewer), a frequency table is a useful summary in its own right. Unlike frequency tables for continuous data, no grouping is involved so no information is lost.
Calculating the mean from a frequency table
The mean of a discrete data set can be easily calculated from a frequency table.
The following frequency table describes the sizes of 600 groups of one species of parrot that were observed in Queensland.
Group size x |
Frequency ƒx |
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total | 600 |
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The mean group size is found by adding the sizes of all 600 groups of parrot then dividing by 600,
Note that the numerator, 1760, is the total number of parrots in the 600
groups, so the mean number of parrots per sighting, ,
equals the total number of parrots divided by the total number of groups observed.
The second line in the above calculation can be generalised to give the folowing formula for the mean, based on a frequency table.
where the summation is over the distinct values in the data set, rather than all individuals.
Note that the mean number of parrots per group is not a whole number. This is perfectly reasonable for the mean of a discrete variable.
Using a spreadsheet (Optional)
The above calculation can be easily performed on a spreadsheet. The diagram below indicates how this may be done using Microsoft Excel.
Calculating the standard deviation
A similar simplification holds for the standard deviation of a discrete data set, making use of the formula
Note that the summation on the left would be over all 600 groups of parrot, whereas the summation on the right is only over the 7 distinct group sizes.
A spreadsheet is again a convenient way to perform the calculations.