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Frequency Polygons

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on frequency polygons helps you revise drawing frequency polygons. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA and Edexcel. Plot each frequency at the midpoint of its class and join with lines.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A frequency polygon displays grouped continuous data by plotting the midpoint of each class against its frequency and joining the points with straight lines.

The midpoints are essential. Plotting at the class boundaries instead would misrepresent where the data actually sits, and it is the commonest error in the topic.

Frequency polygons are especially useful for comparing two distributions, since both can be drawn on the same axes without obscuring each other — something overlapping histograms cannot do.

Revision notes

Plotting the points

Find the midpoint of each class, then plot it against that class's frequency.

For the class \(10 \le x < 20\) with frequency \(8\), plot the point \((15, 8)\).

Joining the points

Join consecutive points with straight lines using a ruler.

Do not join back to the axis or close the shape, unless the question specifically asks for it. The polygon is an open line, not a closed figure.

Comparing distributions

Two frequency polygons can be drawn on the same axes with a key.

Comparing their peaks shows which distribution is centred higher, and comparing their spreads shows which is more consistent.

Key points

  • Plot the midpoint of each class.
  • Plot midpoint against frequency.
  • Join points with straight lines.
  • Do not close the shape.
  • Used for grouped continuous data.
  • Two polygons can be compared on the same axes.

Worked examples

Example 1

Find the point to plot for the class \(20 \le x < 30\) with frequency \(12\).

Working

\[\frac{20+30}{2} = 25\]find the class midpoint
\[(25, 12)\]plot midpoint against frequency

Example 2

Find the point to plot for the class \(0 \le x < 10\) with frequency \(7\).

Working

\[\frac{0+10}{2} = 5\]find the class midpoint
\[(5, 7)\]plot midpoint against frequency

Example 3

Why are midpoints used rather than class boundaries?

Working

\[\text{The midpoint represents the class}\]it is the typical value in that range
\[\text{Boundaries would misrepresent the data}\]explain the reason

Common mistakes

  • Plotting at the class boundaries.

    The midpoint represents the class, so plot there.

  • Joining the ends back to the axis.

    The polygon is an open line unless the question says otherwise.

  • Using a curve instead of straight lines.

    Consecutive points are joined with straight lines.

  • Using it for categorical data.

    Frequency polygons are for grouped continuous data.

Exam tips

  • Add a midpoint column to the table before plotting.
  • Use a ruler to join consecutive points.
  • Add a key when comparing two distributions.
  • Label both axes clearly.

Key terms

Frequency polygon
A line graph of midpoints against frequencies.
Midpoint
The value halfway through a class.
Continuous data
Data that can take any value in a range.
Distribution
How the data is spread across the classes.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.