Introduction to Frequency Distributions
When we collect data, it quickly becomes unwieldy in raw form. A frequency distribution organises data into a structured table, making patterns and trends much easier to identify.
Frequency Distribution: A table that lists each possible value (or range of values) alongside the number of times it occurs in a dataset, often including relative frequencies (proportions).
There are two main types of data to consider:
- Discrete data , data that can only take specific, separate values (e.g. number of siblings, shoe size, goals scored)
- Continuous data , data that can take any value within a range (e.g. height, time, temperature)
The structure of your frequency table depends on which type of data you have.
Frequency Tables for Discrete Data
For discrete data, each possible value (or category) gets its own row in the table. A well-constructed discrete frequency table includes:
- Value , the possible outcomes of the variable
- Frequency () , the count of how often each value appears
- Relative frequency , the proportion of the total, calculated as
Example: Number of pets owned by 20 students
| Number of pets | Frequency () | Relative Frequency |
|---|---|---|
| 0 | 6 | 0.30 |
| 1 | 8 | 0.40 |
| 2 | 4 | 0.20 |
| 3 | 2 | 0.10 |
| Total | 20 | 1.00 |
Relative frequency for "1 pet":
The relative frequency column always sums to 1 (or 100% if expressed as a percentage). This is a useful check!
Always verify your frequency column sums to the total number of data points (). If it doesn't, you've made an error somewhere.