Grouped Frequency Tables
(KS3, Year 7)

A grouped frequency table is a frequency table where the numbers are grouped together. It shows you how often numbers within each group appear in a list of numbers. Imagine you had a set of numbers:

A grouped frequency table is a way to present this data in a simpler way:

Understanding the Grouped Frequency Table

Rather than showing how many times each number appears in a list of numbers (like a frequency table), a grouped frequency table groups the numbers in the list into different groups, and tells you how many times numbers from within each group appear in the list. Let's look again at our list of numbers (rearranged in order and each group of numbers counted):

• We see that there are 2 numbers that appear in the 1 - 5 group (2 and 5). We write 1 - 5 in the Group column. We write 2 in the Frequency column because numbers in the 1 - 5 range appear 2 times in the list of numbers.
  
  
• We see that there are 4 numbers in the 6 - 10 group (7, 8, 9 and 10). We write 6 - 10 in the Group column. We write 4 in the Frequency column because numbers in the 6 - 10 range appear 4 times in the list of numbers.
  
  

The cumulative frequency table is complete when all numbers and their frequencies have been entered:

Finding Averages from a Grouped Frequency Table

The grouped frequency table can be used to find the average of a set of numbers. A grouped frequency table can be used to find the mean, the median group and the mode group.

Other Types of Frequency Table

• A frequency table shows how often (how frequently) each number appears in a list of numbers.
  
  
• A cumulative frequency table has another column which keeps a running total of the frequencies.
  
  
• A cumulative grouped frequency table is a grouped frequency table that has another column which keeps a running total of the frequencies.
  
  

Note

What's in a Name?

"Frequency" means how often something occurs.

Other Column Headings

In the frequency table, the column headings are Group and Frequency. This needn't be the case. Each group is a grouping of numbers. The numbers could represent many things: test scores, incomes, heights, number of pets. Use a descriptive heading in the frequency table (Score, Income, Height, No. of pets).