In the following table, the "cf" column presents cumulative frequencies and the "c%" column presents cumulative percentages.
X f cf c%
5 1 20 100%
4 5 19 95%
3 8 14 70%
2 4 6 30%
1 2 2 10%
A "cf" value of a category is the sum of the frequencies in the categories at and below the category in question.
A "c%" value of a category is 100 times the cumulative frequency of the category, divided by the total frequency. That is
It is possible to determine some percentile ranks directly from the frequency distribution table, provided that the percentile ranks are percentages that appear in the table.
For example, the percentile rank of X=3.5 is 70% (note that 3.5 is the upper real limit of the category where X=3).
It is also possible to determine some percentiles directly from the frequency distribution table, provided that the percentiles are upper real limits of a category.
Thus, the 95th percentile is X=4.5, the upper real limit of the X=4 category.
The interpolation process is explained in the textbook on pages 54-57.