3.2 Frequency polygons
If you have the right sort of grouped, numerical data to draw a histogram, you could also draw a frequency polygon: plot the frequencies at the midpoint of each class and join them with straight lines. You may associate the word polygon with shapes; a frequency polygon shows the shape of the frequency distribution. The diagram below shows the histogram from Activity 7; the black line joining the midpoints of the bars is the frequency polygon for this data, which clearly shows the peak of the data is in the 20 – 40-year-old group.
It is not necessary to keep the bars visible underneath a frequency polygon, so it is visually simpler than a histogram. Often you will see multiple frequency polygons drawn on the same axes for comparison, which is not possible for a histogram.
Watch out for learners mistakenly joining the first and last points to each other or to the x-axis “because it’s a polygon.” An understandable mistake, but it’s not that sort of polygon!
Activity 8
Here are two frequency polygons representing the age demographic of two different villages, drawn on the same axes.
Use the graph to answer the following questions Which village is the one you have been using for the play park investigation in this course?
Multiple choice: A or B Use the information shown on the graph to identify in which village it might be more appropriate to develop a play park, giving a reason for your answer.
Answer
Village A One possible answer here Village A because this village appears to have a younger age demographic than Village B, as shown by the blue line being higher than the orange line for the under 40 age categories. Although, you could also argue that developing the play park in Village B would be more sensible since the aging population might mean more properties become available in the future encouraging younger families to move to the village.