Triangular graphs

Overview

What kind of data a triangular graph takes, why the three values must total 100, how a point is read and plotted, and what the vertices and the centre each mean.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is a triangular graph, and what kind of data can be plotted on it?

   Model answer

   A triangular graph is an equilateral triangle in which each of the three sides is an axis running from 0 to 100 per cent. It plots data made up of exactly three components that together account for the whole of something, with one single point representing all three values at once. Typical uses are the proportion of a workforce in primary, secondary and tertiary employment; the sand, silt and clay content of a soil; and the proportion of a population in three age bands.

2. 2

   Why must the three values sum to 100 before they can be plotted on a triangular graph?

   Model answer

   Because the geometry of the triangle only works for a closed set of three proportions: the position of a point is fixed by the fact that the three readings taken from the three axes always add to 100. If the values do not sum to 100 - because they are absolute totals, or because a fourth category has been left out - no point on the triangle can represent them, and any point plotted will be false. Raw figures must therefore be converted to percentages of their own total first.

3. 3

   How do you read the three values off a single point on a triangular graph?

   Model answer

   Take one axis at a time. For each axis, follow the set of gridlines that run parallel to the side opposite the vertex where that component reads 100 per cent, find the line that passes through the point, and read where that line meets the axis - that is the percentage for that component. Repeat for the second and third axes. The three readings must add to 100; if they do not, you have followed the wrong set of gridlines for at least one axis, and should re-read them.

4. 4

   What is the mistake students most often make when reading a triangular graph?

   Model answer

   Following the wrong set of gridlines - reading a value by moving in the direction the eye finds natural rather than along the lines that belong to that axis, which usually gives the value for a different component. The second common error is ignoring the direction in which an axis is numbered, since each axis increases towards one particular vertex and the numbering runs the opposite way to what is expected. The reliable safeguard is arithmetic: read all three, add them, and if the total is not 100, the reading is wrong.

5. 5

   How do you plot a new point on a triangular graph?

   Model answer

   Take the first component and find its value on its own axis, then draw or trace a line from there running parallel to the side opposite the vertex where that component reads 100 per cent. Do the same for the second component from its axis. The point where the two lines cross is the plotted point, and its position should automatically give the correct value for the third component when read off, which is the check that the plot is right.

6. 6

   What does a point plotted at one of the vertices of a triangular graph mean?

   Model answer

   It means that one component accounts for 100 per cent of the total and the other two are zero. A point near a vertex therefore indicates overwhelming dominance by that one component - a soil that is almost entirely clay, or an economy in which almost the whole workforce is in one sector - and the closer to the vertex, the more extreme the dominance.

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