Reports and Visualizations

Gravetter & Wallnau, Chapter 2; Young, Chapter 2

Copyright © 1997-8 by Forrest W. Young.

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Percentiles & Percentile Ranks

In order to define what we mean by percentiles and percentile ranks, we first begin by defining cumulative frequencies and cumulative percentages.

Cumulative Frequencies
The cumulative frequency of a particular category in a frequency table or distribution is the number of observations in or below that category.

Cumulative Percentages
The cumulative percentage of a particular category in a frequency table or distribution is the percentage of observations in or below that category.

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 

c%=100*(cf/N)

Percentile Rank
The percentile rank of a particular score is defined as the percentage of the scores in a distribution which are at or below the particular score.

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).

Percentile
When a score is identified by its percentile rank, the score is called a percentile.

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.

Interpolation
The process known as interpolation must be used to estimate percentile ranks and percentile for values not given in the table.

The interpolation process is explained in the textbook on pages 54-57.

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