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'):
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:
and thus, we can consider
Smoke to be an ordinal categorical variable. The frequency and relative frequency tables are both presented below:
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 (%)|
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? %
- 47 (The answer can be calculated as follows: \(19 + 17 + 11\))
- 19.92 (or 19.91). The answer can be calculated as follows: \(100 - 80.08\) OR \(8.05 + 7.2 + 4.66\)