2.2 Frequency, relative frequency and cumulative tables for ordinal data
Consider another variable from the survey
data set called Smoke
, which indicates how much a student smokes. This categorical variable can take the following values (or 'levels'):
 Heavy
 Regularly
 Occasionally
 Never
The levels presented above are in an arbitrary order. However, it would make sense to present them from least regular to most regular as follows:
 Never
 Occasionally
 Regularly
 Heavy
and thus, we can consider Smoke
to be an ordinal categorical variable. The frequency and relative frequency tables are both presented below:


Since the Smoke
variable is ordinal, it can be useful to convert our frequency and relative frequency tables into cumulative tables, so that as the categories go up, the values are added together. Such tables are called cumulative frequency tables and cumulative relative frequency tables respectively. Putting it all together, we could present the four types of tables together in one table as below:
Smoke  Frequency  Cumulative Frequency  Relative Frequency (%)  Cumulative Relative Frequency (%) 

Never  189  189  80.08  80.08 
Occasionally  19  208  8.05  88.14 
Regularly  17  225  7.20  95.34 
Heavy  11  236  4.66  100.00 
Test your knowledge
Use Table 2.4 to answer the following questions (please give answers to 2 decimal places where relevant):
 How many students smoke occasionally?
 How many students do not smoke heavily?
 How many students smoke at least occasionally?
 What percentage of students smoke regularly? %
 What percentage of students do not smoke regularly? %
 What percentage of students smoke at least occasionally? %
 19
 225
 47 (The answer can be calculated as follows: \(19 + 17 + 11\))
 7.2
 92.8
 19.92 (or 19.91). The answer can be calculated as follows: \(100  80.08\) OR \(8.05 + 7.2 + 4.66\)