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# Frequency Polygons

### Frequency Polygons

Frequency polygons are a method of visually representing frequency values for categories or intervals.

Another way to represent frequencies of groups and categories is by drawing **frequency polygons**. These can be used for **both** discrete and continuous data, and represent data in a very simple way.

Zac records the number of miles he walks in a table

This is **discrete** data, which means we can easily translate this to a frequency polygon without much further effort. All we need to do is generate points.

Frequency belongs on the y-axis

Therefore, to find the coordinates, use the number of miles as the x-coordinate, and the frequency for the y-coordinate.

What are the coordinates for 4 miles walked?

What are the coordinates for 5 miles walked?

This the full set of coordinates

Now we can look to plot these on a frequency polygon!

We can also use a frequency polygon to represent continuous data.

A class is asked about the amount of pocket money they receive each week

We can see the data is continuous. There are 2 students that receive an amount between £0 and £5, but we don't know exactly how much. This would therefore be hard to plot on a graph.

To plot this on a graph, use midpoints

Choose the midpoint of each interval. This gives the fairest estimate. For example, the midpoint of the interval $20<x\leq25$ is $\dfrac{20+25}{2}=22.5$

What is the midpoint of the interval $15<x\leq20$?

Now we have our coordinates

The midpoint value should be the x-coordinate, while the frequency should be the y-coordinate.