- Create frequency tables to display data
Frequency Tables
Frequency tables are valuable tools in statistics for organizing and summarizing categorical data. They present a clear picture of how frequently each category appears in a data set, allowing us to identify patterns and gain insights from the information. Let’s dive into the components of a frequency table and learn how to construct and interpret one.
Components of a Frequency Table
A frequency table consists of two main components:
- Categories: These are the distinct groups or categories that the data fall into. For example, in a survey asking people about their favorite colors, the categories might be red, blue, green, yellow, and so on.
- Frequencies: The frequencies represent the number of occurrences of each category in the dataset. Frequencies indicate how many times each category appears in the data.
Favorite Foods
Suppose data was collected asking a small group of young adults about their favorite cuisines. The responses were: Indian, Chinese, Mexican, Italian, Thai, Italian, Korean, Indian, Mexican, Vietnamese, Ethiopian, Thai, Chinese, Indian, Korean, Mexican, Ethiopian, Italian, Thai, Indian, and Chinese. To create a frequency table, start by identifying the distinct categories in the data. In our example, the categories will represent the various cuisines. We can determine the number of categories needed by highlighting the first example of each new cuisine type:
Indian, Chinese, Mexican, Italian, Thai, Italian, Korean, Indian, Mexican, Vietnamese, Ethiopian, Thai, Chinese, Indian, Korean, Mexican, Ethiopian, Italian, Thai, Indian, Chinese.
The first row or first column of a two-way frequency table is the category, and the second row or column is the frequency.
| Cuisine | Frequency |
|---|---|
| Chinese | |
| Ethiopian | |
| Indian | |
| Italian | |
| Korean | |
| Mexican | |
| Thai | |
| Vietnamese |
Next, count how many times each cuisine appears in the data and record the frequencies in the table.
| Cuisine | Frequency |
|---|---|
| Chinese | 3 |
| Ethiopian | 2 |
| Indian | 4 |
| Italian | 3 |
| Korean | 2 |
| Mexican | 3 |
| Thai | 3 |
| Vietnamese | 1 |
Two-Way Frequency Tables
A two-way frequency table consists of three main components:
- Row categories: These represent one of the categories data has been collected on.
- Column categories: These represent another of the categories.
- Frequencies: The frequencies represent the number of occurrences for each combination of row and column categories.
| Age group | Favorite genre |
|---|---|
| 13-15 | Fantasy |
| 16-18 | Mystery |
| 13-15 | Adventure |
| 16-18 | Fantasy |
| 13-15 | Mystery |
| 19-21 | Adventure |
| 16-18 | Fantasy |
| 13-15 | Mystery |
| 19-21 | Fantasy |
| 16-18 | Mystery |
We can create a two-way frequency table with age groups for rows and genres for columns:
| Age group | Genre | ||
| Adventure | Fantasy | Mystery | |
| 13-15 | 1 | 1 | 2 |
| 16-18 | 0 | 2 | 2 |
| 19-21 | 1 | 1 | 0 |
… or we can reverse the categories:
| Genre | Age group | ||
| 13-15 | 16-18 | 19-21 | |
| Adventure | 1 | 0 | 1 |
| Fantasy | 1 | 2 | 1 |
| Mystery | 2 | 2 | 0 |
The frequencies in a two-way frequency table are referred to as a joint frequency because they represent an observation in two categories simultaneously.