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Maths Gcse Wjec-Eduqas Higher

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Higher
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Exam code:C300

Frequency polygons

What are the key features of a frequency polygon?

  • 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

  • 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!

  • You may be asked to draw a frequency polygon and/or use it to make comments and compare data

How do I draw a frequency polygon?

  • This is easiest shown by an example

    • e.g. The lengths of 59 songs, in seconds, are recorded in the table below

Song length
t seconds

Frequency

120 ≤ t < 150

4

150 ≤ t < 180

10

180 ≤ t < 210

24

210 ≤ t < 240

18

240 ≤ t < 270

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

How do I use and interpret a frequency polygon?

  • Think about what you could you say about the data above, particularly by looking at the diagram only?

    • The two things to look for are averages and spread

      • The modal class is 180 ≤ t < 210

      • It would be acceptable to say that 195 seconds is (an estimate of) the modal song length

      • The diagram (rather than the table) shows (an estimate of) the range of song lengths is 255 – 135 = 120 seconds

      • If 2 frequency polygons are drawn on the same graph comparisons between the 2 sets of data can be made

Examiner Tips and Tricks

  • 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

A local council ran a campaign to encourage households to waste less food.
To compare the impact of the campaign the council recorded the weight of food waste produced by 30 households in a week both before and after the campaign.
The results are shown in the table below.

Food waste
w kg

Frequency
(before campaign)

Frequency
(after campaign)

1 ≤ w < 1.4

3

5

1.4 ≤ w < 1.8

4

8

1.8 ≤ w < 2.2

8

14

2.2 ≤ w < 2.6

10

3

2.6 ≤ w < 3

5

1

a)

On the same diagram, draw two frequency polygons, one for before the council’s campaign and one for after.

Food-Waste-FP, downloadable IGCSE & GCSE Maths revision notes

Remember to include a key to show which frequency polygon is which.

b)

Comment on whether you think the council’s campaign has been successful or not and give a reason why.

The council campaign has been successful as the modal amount of waste has reduced from 2.4 kg of food waste per week to 2 kg

Remember to look for average(s) and/or spread – the mode (average) is appropriate in this case.

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