One of the ways to display grouped data – that which is usually given in a grouped frequency table – is by using a frequency polygon. They’re nothing to worry about, so here we’ll have a quick look at how to go about drawing one.

Example: Data was collected on the ages of the attendees of a local swimming pool. The results are recorded in the grouped frequency table below. Construct a frequency polygon of this data.

The first step towards constructing a frequency polygon is to add another column to this table:

MIDPOINTS

The midpoint of any group is the number that lies halfway between the two boundaries. For the first group, halfway between 0 and 16 is 8 – this is the midpoint. In situations where the midpoint is unclear, simply add up the two values and divide by 2. For the second group, we get

Continuing this for the rest of the groups, we get the table with the new column shown here on the right. Now we can start drawing!

Firstly, draw a set of axes with frequency on the y-axis (this will always be the case), and age on the x-axis. Once this is done, we want to plot one point for each group.

The x-coordinate of each point will be the midpoint, while the y-coordinate will be the frequency. Plotting these points correctly, and joining them with straight lines, we get the completed frequency polygon below.

Voila! The process of drawing a frequency polygon effectively boils down to:

1. Find the midpoints;

2. Plot the midpoints against the frequencies;

3. Join the points with straight lines.

Read through this example again if you’re not completely comfortable with the process, and once you think you’ve got it down, have a go at the questions below.

### Example Questions

Firstly, we need to add on a “midpoints” column to our table. Each of these groups fall between multiples of 10, so the midpoints shouldn’t be too difficult to find. The result is the table below.

Now, plotting the midpoints on the x-axis and the frequency values on the y-axis then joining the points with straight lines, we get the frequency polygon shown below.

Firstly, we need to add on a “midpoints” column to our table. Each of these groups is 1 wide, so the halfway points will just be halfway between the whole numbers: 0.5, 1.5, and so on. The resulting table is shown below.

Now, plotting the midpoints on the x-axis and the frequency values on the y-axis then joining the points with straight lines, we get the frequency polygon shown below.

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