Frequency tables and frequency diagrams
When a lot of Values, typically letters or numbers. needs to be sorted, one of the most efficient ways is to use a frequency table.
It is important to consider the sizes of groups when sorting data into 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..
Example
Megan owns a bakery. She counts the number of customers she has each day at lunchtime on 30 consecutive days. The results are shown here.
| 13 | 8 | 16 | 12 | 12 | 16 |
| 7 | 18 | 11 | 16 | 15 | 7 |
| 11 | 12 | 13 | 21 | 17 | 19 |
| 11 | 14 | 10 | 19 | 13 | 12 |
| 7 | 16 | 6 | 14 | 12 | 18 |
| 13 |
| 8 |
| 16 |
| 12 |
| 12 |
| 16 |
| 7 |
| 18 |
| 11 |
| 16 |
| 15 |
| 7 |
| 11 |
| 12 |
| 13 |
| 21 |
| 17 |
| 19 |
| 11 |
| 14 |
| 10 |
| 19 |
| 13 |
| 12 |
| 7 |
| 16 |
| 6 |
| 14 |
| 12 |
| 18 |
Using this data in list form could be time consuming and with a large set of data it may lead to mistakes or miscalculations. A grouped frequency table would help to display and give an overview of the data. The smallest number is 6 and the biggest number is 21, so groups that have a width of 5 are reasonable. This will give four groups as shown below. Of course, smaller groups would be more accurate but there may be too many groups to show up any pattern in the data.
| Number of customers | Tally | Frequency |
| 5-10 | \(\cancel{||||}~|\) | 6 |
| 11-15 | \(\cancel{||||}~\cancel{||||}~||||\) | 14 |
| 16-20 | \(\cancel{||||}~||||\) | 9 |
| 21-25 | \(|\) | 1 |
| Number of customers | 5-10 |
|---|---|
| Tally | \(\cancel{||||}~|\) |
| Frequency | 6 |
| Number of customers | 11-15 |
|---|---|
| Tally | \(\cancel{||||}~\cancel{||||}~||||\) |
| Frequency | 14 |
| Number of customers | 16-20 |
|---|---|
| Tally | \(\cancel{||||}~||||\) |
| Frequency | 9 |
| Number of customers | 21-25 |
|---|---|
| Tally | \(|\) |
| Frequency | 1 |
Frequency diagrams
A frequency diagram, often called a line chart or a frequency polygon, shows the frequencies for different groups. The frequency chart below shows the results of the table. To plot a frequency polygon of grouped data, plot the frequency at the midpoint of each group.