Relative Frequency Distribution of Qualitative Data

The relative frequency distribution of a data variable is a summary of the frequency proportion in a collection of non-overlapping categories.

The relationship of frequency and relative frequency is:

Relative F requency =-Frequency- Sample Size

Example

In the data set painters, the relative frequency distribution of the School variable is a summary of the proportion of painters in each school.

Problem

Find the relative frequency distribution of the painter schools in the data set painters.

Solution

We first apply the table function to compute the frequency distribution of the School variable.

> library(MASS)                 # load the MASS package
> school = painters$School      # the painter schools
> school.freq = table(school)   # apply the table function

Then we find the sample size of painters with the nrow function, and divide the frequency distribution with it. Therefore the relative frequency distribution is:

> school.relfreq = school.freq / nrow(painters)

Answer

The relative frequency distribution of the schools is:

> school.relfreq
school
A B C D E F
0.185185 0.111111 0.111111 0.185185 0.129630 0.074074
G H
0.129630 0.074074

Enhanced Solution

We can print with fewer digits and make it more readable by setting the digits option.

> old = options(digits=1)
> school.relfreq
school
A B C D E F G H
0.19 0.11 0.11 0.19 0.13 0.07 0.13 0.07
> options(old)

In addition, we can apply the cbind function to print the result in column format.

> old = options(digits=1)
> cbind(school.relfreq)
  school.relfreq
A           0.19
B           0.11
C           0.11
D           0.19
E           0.13
F           0.07
G           0.13
H           0.07
> options(old)    # restore the old option

Exercise

Find the relative frequency distribution of the composition scores in painters.

Tags:

An R Introduction to Statistics