Statistics
A The total of the tally marks is called the frequency, which is shown in an addition column to the right. With this extra-column, the table is called a frequency table. helps us to organise and order data. We often use A system of counting where every group of four vertical lines is followed by a horizontal line to easily count in steps of five. 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:
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
Organise the data in a frequency table in order to help us see at a glance how many of each size there were.
| Size | Tally | Frequency |
| 4 | \(1\) | 1 |
| 5 | \(4\) | 4 |
| 6 | \(3\) | 3 |
| 7 | \(3\) | 3 |
| 8 | \(8\) | 8 |
| 9 | \(7\) | 7 |
| 10 | \(4\) | 4 |
| Size | 4 |
|---|---|
| Tally | \(1\) |
| Frequency | 1 |
| Size | 5 |
|---|---|
| Tally | \(4\) |
| Frequency | 4 |
| Size | 6 |
|---|---|
| Tally | \(3\) |
| Frequency | 3 |
| Size | 7 |
|---|---|
| Tally | \(3\) |
| Frequency | 3 |
| Size | 8 |
|---|---|
| Tally | \(8\) |
| Frequency | 8 |
| Size | 9 |
|---|---|
| Tally | \(7\) |
| Frequency | 7 |
| Size | 10 |
|---|---|
| Tally | \(4\) |
| Frequency | 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 |
| 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:
| Age | Number of people |
| 11 - 20 | 9 |
| 21 - 30 | 16 |
| 31 - 40 | 12 |
| 41 - 50 | 4 |
| 51 - 60 | 6 |
| 61 - 70 | 1 |
| Age | 11 - 20 |
|---|---|
| Number of people | 9 |
| Age | 21 - 30 |
|---|---|
| Number of people | 16 |
| Age | 31 - 40 |
|---|---|
| Number of people | 12 |
| Age | 41 - 50 |
|---|---|
| Number of people | 4 |
| Age | 51 - 60 |
|---|---|
| Number of people | 6 |
| Age | 61 - 70 |
|---|---|
| Number of people | 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:
Question
Here is the data for the length of time people took to fill in an application form to the nearest minute.
| 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) |
| 23,17,15,29,22,21,20,12,19,28,18,18,22,31,13,24,23,18,17,26, 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).
| Length of time (minutes) | Number of people |
| 11-15 | 3 |
| 16-20 | 12 |
| 21-25 | 10 |
| 26-30 | 3 |
| 31-35 | 2 |
| Length of time (minutes) |
| Number of people |
| 11-15 |
| 3 |
| 16-20 |
| 12 |
| 21-25 |
| 10 |
| 26-30 |
| 3 |
| 31-35 |
| 2 |
