Frequency table
A frequency table helps us to organise and order data. We often use tally marks to help us construct frequency tables.
Example
A teacher conducted a survey of shoe sizes of an S1 class. The results are shown below:
| Shoe sizes of S1 class |
| \(9, 8, 7, 8, 9, 9, 8\) |
| \(7, 5, 10, 8, 8, 6, 6\) |
| \(10, 5, 8, 6, 6, 10, 5\) |
| \(8, 9, 9, 10, 10, 8, 5\) |
| \(7, 6, 9, 8, 5, 4, 9\) |
| Shoe sizes of S1 class | \(9, 8, 7, 8, 9, 9, 8\) |
|---|
| Shoe sizes of S1 class | \(7, 5, 10, 8, 8, 6, 6\) |
|---|
| Shoe sizes of S1 class | \(10, 5, 8, 6, 6, 10, 5\) |
|---|
| Shoe sizes of S1 class | \(8, 9, 9, 10, 10, 8, 5\) |
|---|
| Shoe sizes of S1 class | \(7, 6, 9, 8, 5, 4, 9\) |
|---|
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.
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 |
| \(25, 29, 45, 19, 36, 17, 60, 51, 39, 24, 15, 13, 31, 18, 24, 32\) |
| \(37, 27, 23, 53, 41, 34, 29, 28, 52, 17, 55, 47, 34, 28, 22, 20\) |
| \(64, 39, 38, 33, 24, 16, 27, 19, 26, 27, 25, 32, 26, 48, 54, 35\) |
| Ages of customers in 1 hour period | \(25, 29, 45, 19, 36, 17, 60, 51, 39, 24, 15, 13, 31, 18, 24, 32\) |
|---|
| Ages of customers in 1 hour period | \(37, 27, 23, 53, 41, 34, 29, 28, 52, 17, 55, 47, 34, 28, 22, 20\) |
|---|
| Ages of customers in 1 hour period | \(64, 39, 38, 33, 24, 16, 27, 19, 26, 27, 25, 32, 26, 48, 54, 35\) |
|---|
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:
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:
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) |
| \(23,17,15,29,22,21,20,12,19,28\) |
| \(18,18,22,31,13,24,23,18,17,26\) |
| \(25,16,24,18,16,22,33,17,24,18\) |
| Length of time (minutes) | \(23,17,15,29,22,21,20,12,19,28\) |
|---|
| Length of time (minutes) | \(18,18,22,31,13,24,23,18,17,26\) |
|---|
| Length of time (minutes) | \(25,16,24,18,16,22,33,17,24,18\) |
|---|
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)
