Histograms & Frequency Polygons (CIE IGCSE Maths: Core)

Revision Note

Test yourself

Author

Dan

Last updated

4 March 2023

Histograms

What is grouped data?

You might have lots of different values
To help summarise the data you can group the data into intervals
- For example: If you are measuring the heights of 1000 adults then you could use the groups:
  - Less than 140 cm
  - At least 140 cm but less than 160 cm
  - At least 160 cm but less than 180 cm
  - At least 180 cm

What is a histogram?

A histogram is used when data has been grouped
- For your exam the groups will have equal intervals
A histogram is similar to a bar chart
- The variable (height, length, etc) is plotted on the horizontal axis
- The frequency is plotted on the vertical axis
Rectangular bars are drawn
- The width covers the interval of the group on the horizontal axis
- The height is the frequency
There should be no gaps between the bars of a histogram
- This is different to a bar chart

Worked example

The table below and its corresponding histogram show the mass, in kg, of some new born bottlenose dolphins.

Mass	Frequency
At least 4 kg but less than 8 kg	4
At least 8 kg but less than 12 kg	15
At least 12 kg but less than 16 kg	19
At least 16 kg but less than 20 kg	10
At least 20 kg but less than 24 kg	6

Draw a frequency histogram to represent the data.

Draw rectangular bars with no gaps.

histograms

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Frequency Polygons

What are frequency polygons?

Frequency polygons are a very simple way of showing frequencies for continuous, grouped data and give a quick guide to how frequencies change from one class to the next

What are the key features of a frequency polygon?

The horizontal axis and vertical axis are plotted exactly the same as a histogram
Apart from plotting and joining up points with straight lines there are 2 rules for frequency polygons:
- Plot points at the MIDPOINT of class intervals
- Unless one of the frequencies is 0 do not join the frequency polygon to the x-axis, and do not join the first point to the last one
The result is not actually a polygon but more of an open one that ‘floats’ in mid-air!
If you draw a histogram on the same graph the frequency polygon will join together the middle of the tops of the bars

Examiner Tip

Jot down the midpoints next to the frequencies so you are not trying to work them out in your head while also concentrating on actually plotting the points

Worked example

The lengths of 59 songs, in seconds, are recorded in the table below. Draw a frequency polygon to represent the data.

Song length	Frequency
At least 120 seconds but less than 150 seconds	4
At least 150 seconds but less than 180 seconds	10
At least 180 seconds but less than 210 seconds	24
At least 210 seconds but less than 240 seconds	18
At least 240 seconds but less than 270 seconds	3

Frequencies are plotted at the midpoints of the class intervals, so in this case we would plot the points (135, 4), (165, 10), (195, 24), (225, 18) and (255, 3).
Join these up with straight lines (but do not join the last to the first!)

Song Length FP, IGCSE & GCSE Maths revision notes