A grouped frequency table is a tool used to organize and summarize categorical data, which is data that can be placed into specific categories or groups. It allows us to see the distribution of the data and identify patterns or trends. Here is a step-by-step guide on how to create a grouped frequency table:

Define the categories or groups for your data. These categories should be mutually exclusive, meaning that each piece of data should only belong to one group. For example, if you are collecting data on the favorite colors of a group of people, the categories might be "red," "yellow," "green," "blue," and "other."

Collect and organize the data. Make sure that each piece of data is placed into the appropriate category.

Determine the range of the data. The range is the difference between the highest and lowest values in the data set. For example, if the lowest value is 10 and the highest value is 50, the range is 40.

Divide the range by the number of categories you want to create. This will give you the width of each category or "class interval." For example, if the range is 40 and you want to create 5 categories, the width of each category will be 8 (40 รท 5 = 8).

Determine the lower and upper bounds of each category. The lower bound is the smallest value that can be included in a category, and the upper bound is the largest value that can be included. For example, if the width of each category is 8 and the lowest value is 10, the lower bounds of the categories might be 10, 18, 26, 34, and 42. The upper bounds would be the corresponding values plus 8, so 18, 26, 34, 42, and 50.

Count the number of data points that fall within each category. For example, if you have 20 data points and 5 categories, you might find that 3 data points fall within the first category (lower bound of 10, upper bound of 18), 6 data points fall within the second category (lower bound of 18, upper bound of 26), and so on.

Calculate the frequency of each category. The frequency is the number of data points that fall within each category. In the example above, the frequency of the first category would be 3, the frequency of the second category would be 6, and so on.

Create the grouped frequency table. To do this, you will need to list the categories (or class intervals) on the left side of the table, and the frequencies on the right side. You might also want to include a column for the percentage of the total number of data points that fall within each category.

Here is an example of a grouped frequency table for the data on favorite colors:

Color | Frequency | Percentage |
---|---|---|

Red | 3 | 15% |

Yellow | 6 | 30% |

Green | 4 | 20% |

Blue | 5 | 25% |

Other | 2 | 10% |

Total | 20 | 100% |

This grouped frequency table shows that the most popular color is yellow, followed by blue and green. It also shows that 15% of the people surveyed prefer red, 30% prefer yellow, and so on.

In conclusion, creating a grouped frequency table is a useful way to organize and summarize categorical data. It allows us to see the distribution of the data and identify patterns or trends. By following the steps outlined above, you