Frequency Polygons
A frequency polygon is a line graph used to show the shape of grouped data, drawn by plotting a point at the midpoint of each class interval at a height equal to its frequency, then joining the points with straight lines. It is often used in GCSE Statistics to compare the shape of two or more distributions on the same axes, which is harder to do clearly with histograms or bar charts.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find the midpoint of each class interval by adding the two class boundaries and dividing by 2.
- Plot a point for each class at its midpoint value on the horizontal axis and its frequency on the vertical axis.
- Join the plotted points with straight lines, in order from the lowest class to the highest.
- Do not extend the line beyond the first or last plotted point, unless the task specifically asks you to join to zero frequency at the edges.
- Label both axes clearly, including units, and title the graph.
- To compare two data sets, draw both frequency polygons on the same axes using different line styles, and compare their peaks and spread.
Worked example
The table shows the weights, in kg, of 30 parcels: 0-4 kg freq 4, 4-8 kg freq 10, 8-12 kg freq 12, 12-16 kg freq 4. State the coordinates that would be plotted to draw a frequency polygon for this data.
- Find the midpoint of each class: (0+4)/2 = 2, (4+8)/2 = 6, (8+12)/2 = 10, (12+16)/2 = 14.
- Pair each midpoint with its frequency to get the coordinates: (2, 4), (6, 10), (10, 12) and (14, 4).
- Plot these four points on axes with weight (kg) on the horizontal axis and frequency on the vertical axis.
- Join the points in order with straight lines to complete the frequency polygon.
- Final answer: the plotted points are (2, 4), (6, 10), (10, 12) and (14, 4), joined in that order.
Practice questions
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Q1What value do you plot on the horizontal axis for each class of a frequency polygon?Show answer
Answer: The midpoint of the class interval.
Q2Find the midpoint of the class interval 10-20.Show answer
Answer: 15 ((10+20)/2 = 15).
Q3A class interval is 20-30 with frequency 8. Give the coordinates of the point plotted for this class.Show answer
Answer: (25, 8) (midpoint 25, frequency 8).
Q4A frequency table has classes 0-10, 10-20, 20-30 with frequencies 3, 9, 6. State all three coordinates for the frequency polygon.Show answer
Answer: (5, 3), (15, 9), (25, 6).
Q5Two frequency polygons are drawn on the same axes for boys' and girls' test scores. What feature of the graphs shows which group generally scored higher?Show answer
Answer: Whichever polygon's peak (highest point) is further to the right, along the score axis.
Q6A frequency polygon has classes of unequal width: 0-10 and 10-30. Explain why comparing the heights of the two plotted points directly can be misleading.Show answer
Answer: The classes cover different widths, so equal frequencies would represent very different data densities; the raw heights do not account for this difference in width.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
The table shows the ages, in years, of 40 members of a gym: 10-20 freq 6, 20-30 freq 16, 30-40 freq 12, 40-50 freq 6. State the coordinates that would be plotted to draw a frequency polygon for this data.
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Frequency polygons for the times taken by two groups of runners, Group A and Group B, are drawn on the same axes. Group A's polygon peaks at (35, 18) and Group B's polygon peaks at (25, 15). Compare the typical time taken by each group, and compare which group has the higher single frequency for any time.
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Give one advantage of drawing a frequency polygon rather than a histogram when comparing two data sets.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the frequency polygons worksheet pack - 20 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 20 of GCSE Statistics Foundation Workbook 1 and chapter 24 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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