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Graphical Skills » Triangular Graphs, Proportional Symbols and Diagrams

What you'll learn this session

Study time: 30 minutes

Cambridge spec: Geographical skills, Graphical skills

How to read and plot a triangular graph
How to read radial graphs and proportional symbols
How to read flow, systems and Venn diagrams, and cross-sections in sources
How to choose the right graph for the data

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Triangular graphs

A triangular graph shows three percentages that add up to 100 for one place or one sample. Each corner of the triangle stands for 100% of one thing. The closer a point is to a corner, the more of that thing it has.

Key terms:

Triangular graph: a triangle-shaped graph that plots three percentages adding to 100.
Radial graph: a graph drawn from a centre point, with a spoke for each time or category and the distance from the centre showing the value.
Proportional symbol: a circle or bar whose size is drawn in proportion to the value it shows.
Flow diagram: boxes joined by arrows to show the order of events or the movement of things.
Systems diagram: a diagram that sorts a system into inputs, processes and outputs.
Venn diagram: overlapping circles that show which items belong to one group, another group or both.

Triangular graphs are often used for soil texture (sand, silt and clay) or for employment structure (primary, secondary and tertiary).

Worked example: soil texture

A made-up soil sample is 50% sand, 30% silt and 20% clay.

To plot it: (1) Find 50 on the sand scale and follow its grid line across the triangle. (2) Find 30 on the silt scale and follow its grid line. (3) Mark the point where the two lines cross. (4) Check that the clay grid line through the point reads 20.

To read it: Do the same in reverse. Follow each grid line from the point to its scale, then add the three values. If they do not total 100, you have read a scale wrongly.

To describe it: Say which corner the point is nearest, give the values, and mention anything unusual. Here the point is nearest the sand corner because sand is the largest share at 50%, and clay is the smallest at 20%. Points from several samples that cluster together show a similar mix.

Missing value: You only need two values to plot a point. For a made-up country with 15% in primary jobs and 35% in secondary jobs, tertiary is 100 − 15 − 35 = 50%.

Radial graphs

A radial graph looks like a clock or a spider's web. Each spoke is a time or a category. The further a point is from the centre, the bigger the value. Radial graphs suit data that repeats in a cycle, such as the 24 hours of a day or the 12 months of a year.

Here is made-up data for a town road.

Time	00:00	03:00	06:00	09:00	12:00	15:00	18:00	21:00
Vehicles per hour	20	10	120	200	150	170	220	60

Worked example: traffic over 24 hours

To draw it: (1) Draw eight spokes like a clock face, with 00:00 at the top. (2) Draw rings for the scale, from 0 in the centre to 250 at the edge. (3) Mark each value on its spoke. (4) Join the points to make a shape. (5) Add a title.

To describe it: Traffic is lowest at 03:00 with 10 vehicles an hour. There are two peaks, 200 at 09:00 and 220 at 18:00, which fit the journeys to and from work and school. Traffic then falls quickly to 60 at 21:00.

Proportional symbols

Proportional symbols show how big a value is by the size of the symbol. They are often placed on a map, so you see where the big values are as well as how big they are.

📊 Bars

Bar height is in proportion to the value. If 1 cm stands for 1 million people, then 4 cm stands for 4 million.

🌕 Circles

Circle area is in proportion to the value. A value 4 times bigger gives a circle with 4 times the area but only 2 times the width.

Worked example: city sizes

On a made-up map, City P has 1 million people and a circle 1 cm wide. City Q has 4 million, so its circle is 2 cm wide. City R has 9 million, so its circle is 3 cm wide.

To read it: Always use the key. Compare the circle with the key circles and estimate the value. Do not say the circle is “twice as big” unless its area is twice as big.

To describe it: Name the biggest and smallest symbols and where they are. Here City R is the biggest and City P is the smallest, so the 9 million city has nine times the area of the 1 million city.

Flow diagrams and systems diagrams

🔄 Flow diagram

Boxes joined by arrows show the order things happen in, or where things move from and to. Arrows can be drawn wider to show a bigger flow. Read it by following the arrows from the start.

📦 Systems diagram

It sorts a system into inputs, processes and outputs, as in the lesson Farming as a System. Read it from left to right and put each item in the right column.

Worked example: a town's water supply

Systems diagram: Inputs are rain and river water. Processes are storing the water in a reservoir and cleaning it at a treatment works. Outputs are tap water for homes and waste water going to the sewers.

Flow diagram of the same story: Rain falls, then the river fills the reservoir, then the water is treated, then it is piped to homes, then waste water goes to the sewer. Each step is a box and each arrow points to the next one.

Venn diagrams

A Venn diagram uses overlapping circles. Each circle is a group. The part where circles overlap holds items that belong to both groups. Items outside the circles belong to neither.

Worked example: made-up villages

Five villages are checked for a school and a health clinic. Ashby and Brent have a school only. Calder and Dunmore have both. Eston has a clinic only.

To draw it: Circle 1 is “school” and circle 2 is “clinic”. Ashby and Brent go in the school circle only. Calder and Dunmore go in the overlap. Eston goes in the clinic circle only.

To read it: Two villages have both services. Only Eston has no school.

Reading a cross-section in a source

A cross-section is a side view of the land. Drawing one is covered in the lesson Contours, Gradient and Cross-Sections. In a source you read it like this: (1) check the title and both axes with their units; (2) pick out the distance and height of the labelled features; (3) describe the high points, the low points and where the slopes are steep or gentle.

Worked example: a made-up valley

Heights are 180 m at 0 km, 90 m at 1 km, 30 m at 2 km (the river), 70 m at 3 km and 200 m at 4 km.

To describe it: The land falls 150 m, from 180 m to 30 m, over the first 2 km to reach the river. It then climbs 170 m over the next 2 km to 200 m. The right-hand side is a little steeper and higher than the left.

Choosing the right graph

Ask what the data is like, then pick the graph that shows it best. The common graphs are in the lesson Drawing and Reading Graphs.

The data is...	Best choice
Three percentages that add to 100	Triangular graph
Values that repeat over 24 hours or 12 months	Radial graph
Values for places on a map	Proportional symbols
Steps in an order, or movements	Flow diagram
Things going in, being changed and coming out	Systems diagram
Items that fit in one group, another or both	Venn diagram

Common mistakes

Triangular graph: reading the wrong scale, or giving three values that do not add to 100. Radial graph: joining the last point to the wrong spoke, or reading a value from the spoke instead of the ring. Proportional symbols: drawing a circle with twice the width for twice the value, which gives four times the area. Flow and systems diagrams: arrows pointing the wrong way, or an output put under inputs. Venn diagram: putting items from both groups in only one circle.

Exam-style question

Fig. 1.1 is a made-up table of data for Country W.

Employment sector	Primary	Secondary	Tertiary
Percentage of workers	12	28	?

(a) Calculate the percentage of workers in the tertiary sector. [1]

(b) Describe how you would plot Country W on a triangular graph. [2]

(d) Justify the best graph or diagram to show each set of data below. Give a reason for each. [6]

The percentages of sand, silt and clay in a soil.
The populations of six cities placed on a map.
Which of 20 villages have a school, a clinic or both.

Model answer

(a) 100 − 12 − 28 = 60% (1)

(b) Find 12 on the primary scale and follow its grid line (1). Find 28 on the secondary scale and mark where the two lines cross (1).

(d) Other suitable graphs are credited if the reason is valid. Soil: a triangular graph (1) because the three percentages add to 100 (1). Cities: proportional symbols on a map (1) because the symbol size shows each population and its position shows where the city is (1). Villages: a Venn diagram (1) because it shows which villages are in one group, the other or the overlap (1).

Exam tip

In a “justify” question, name the graph and then give a reason that links to the data. In this question each choice earns one mark for the graph and one for the reason.

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