Sheet № 238 · Foundation + Higher · AQA · Edexcel · OCR
Frequency Polygons –
Frequency polygons appear regularly on GCSE Maths papers at Foundation and Higher tier. They are a quick way to display grouped data and are especially useful when you need to compare two distributions on the same axes. Unlike bar charts, frequency polygons use a single plotted line, making overlapping comparisons much clearer. This guide
§Key definitions
Question:
The table shows the masses (g) of 50 apples.
Answer:
A line graph with five plotted points joined in order, peaking at (129.5, 18).
Average:
Class B's peak and general position are further to the right, suggesting Class B scored higher on average.
Spread:
Class A's data is concentrated between 35 and 65 (a range of 30 marks), while Class B spans 45 to 85 (a range of 40 marks). Class B's results are more spread out.
Q1 (Foundation):
A grouped frequency table for the time (minutes) spent on homework by 40 students has classes 0–9, 10–19, 20–29, 30–39 with frequencies 4, 14, 16, 6. Find the midpoints and plot the frequency polygon.
§Formulas to memorise
Midpoint = (lower bound + upper bound) ÷ 2
Calculate the midpoint — of each class interval.
Plot each point — at (midpoint, frequency) on a grid.
Join the points — with straight lines in order from left to right.
Label your axes — the horizontal axis shows the data variable with units; the vertical axis shows frequency.
Worked example
The table shows the masses (g) of 50 apples. | Mass (g) | 80–99 | 100–119 | 120–139 | 140–159 | 160–179 | |---|---|---|---|---|---| | Frequency | 5 | 12 | 18 | 10 | 5 | Draw a frequency polygon for this data.
Working:
⚠ Common mistakes
- ✗Plotting at the class boundaries instead of midpoints. The point must be plotted at the midpoint of each class interval, not at the start or end.
- ✗Using unequal class widths without adjusting. If class widths vary, you may need frequency density (see histograms) rather than a frequency polygon.
- ✗Forgetting to label axes or give a title. The examiner will deduct marks for missing labels.
✦ Exam tips
- →Always calculate midpoints first and write them in a table column — this avoids plotting errors.
- →When comparing two distributions, make at least two statements: one about the centre (e.g. "the peak is further to the right") and one about the spread.
- →Use a ruler and plot points as small crosses for accuracy.
- →For grouped data averages, see frequency tables and grouped data. For cumulative frequency, see cumulative frequency and box plots.