Frequency table

A frequency table helps us to organise and order data. We often use tally marks to help us construct frequency tables.

Example

Shoe size tally 4-1, 5-4, 6-3, 7-3, 8-8, 9-7, 10-4

A teacher conducted a survey of shoe sizes of an S1 class. The results are shown below:

Shoe sizes of S1 class
9, 8, 7, 8, 9, 9, 8
7, 5, 10, 8, 8, 6, 6
10, 5, 8, 6, 6, 10, 5
8, 9, 9, 10, 10, 8, 5
7, 6, 9, 8, 5, 4, 9

These results are quite difficult to read. Organising the data in a frequency table helps show at a glance how many of each size there were.

Frequency chart. Size (4, 5, 6, 7, 8, 9, 10). Tally marks. Frequency (1, 4, 3, 3, 8, 7, 4)

Making a frequency table for grouped data

Here is the data for the ages of customers in the Bitesize coffee shop.

Ages of customers in 1 hour period
25, 29, 45, 19, 36, 17, 60, 51, 39, 24, 15, 13, 31, 18, 24, 32
37, 27, 23, 53, 41, 34, 29, 28, 52, 17, 55, 47, 34, 28, 22, 20
64, 39, 38, 33, 24, 16, 27, 19, 26, 27, 25, 32, 26, 48, 54, 35

We could show this data in a table with one number in each row, but it would have a lot of rows!

We can group the ages together so that we have fewer categories.

This is the same set of data put into groups:

Frequency chart. Age (11-20, 21-30, 31-40, 41-50, 51-60, 61-70). Tally marks. Number of people (9, 16, 12, 4, 6, 1)

When choosing intervals for the data sets try not to make the intervals too big or too small.

You could use the above intervals to draw a frequency chart:

Frequency bar chart showing number of people by age
Question

Here is the data for the length of time (to the nearest minute) people took to fill in an application form.

Length of time (minutes)
23,17,15,29,22,21,20,12,19,28
18,18,22,31,13,24,23,18,17,26
25,16,24,18,16,22,33,17,24,18

Make a frequency table of this data.

(The answer below starts with 11-15, 16-20, etc. The interval choice is sometimes up to you)

Frequency chart. Time (11-15, 16-20, 21-25, 26-30, 31-35). Tally marks. Number of people (3, 12, 10, 3, 2)