Frequency tables and frequency diagrams
When there is a lot of data to record, it might be put into groups to speed up the process and to produce more helpful graphs. Too many groups would still take too long, and too few groups would not give enough detail. Between five and eight groups is usually about right.
Example
The frequency table below shows the lengths of 40 babies at birth.
| Length (cm) | Frequency |
| \(30 \textless l \leq 35\) | 4 |
| \(35 \textless l \leq 40\) | 10 |
| \(40 \textless l \leq 45\) | 11 |
| \(45 \textless l \leq 50\) | 12 |
| \(50 \textless l \leq 55\) | 3 |
| Length (cm) | \(30 \textless l \leq 35\) |
|---|---|
| Frequency | 4 |
| Length (cm) | \(35 \textless l \leq 40\) |
|---|---|
| Frequency | 10 |
| Length (cm) | \(40 \textless l \leq 45\) |
|---|---|
| Frequency | 11 |
| Length (cm) | \(45 \textless l \leq 50\) |
|---|---|
| Frequency | 12 |
| Length (cm) | \(50 \textless l \leq 55\) |
|---|---|
| Frequency | 3 |
Notice: five groups, all of the same width. There are no gaps – every length from 30 to 55 can be recorded. There are no overlaps between the groups – eg the inequality symbols show that exactly 35 cm would be recorded in the first group not the second.
The frequency table can now be shown as a frequency diagram.
Frequency polygons
An alternative way of showing this data is to use a frequency polygon. The frequency is plotted against the midpoint of each group and the points are then joined by straight lines.
Example
Using the above table, the midpoints are 32.5, 37.7, 42.5, 47.5 and 52.5. So plot (32.5, 4), (37.5, 10) and so on. It is common (but not essential) to put in extra points at the start and end to show a frequency of 0: (27.5, 0) and (57.5, 0). Then when you join the points together with a straight line, you get a polygon!