Recognising and Critiquing Graphical Misrepresentation

What is your eye measuring?

A chart can be completely accurate in its numbers and still mislead. Every technique in this topic works the same way, and once you see it you stop having to memorise them. **A chart works because your eye reads a visual quantity - a length, a height, an area - and treats it as standing for the number.** **A misleading chart breaks that link.** A truncated axis breaks it by moving where zero is, so height stops being proportional to value. Distorted sizing breaks it by scaling a picture in two directions when only one stands for the number. Plotting frequency as height on unequal classes breaks it by ignoring the width the area depends on. **So ask one question of any chart: what is my eye actually measuring, and is that the number?** It catches all of them, including tricks nobody has shown you.

The named distortions

The specification names these, so use the terms in your answers rather than saying the chart looks wrong.

Same data, two charts

Both charts show the same three values: 100, 105 and 110. **Tap the chart that exaggerates the difference between them.**

Match each distortion to how it misleads

Why the axis matters

A bar chart shows three values, 100, 105 and 110, with the vertical axis starting at 95. What is wrong, and how should a critique put it?

• The axis is truncated, so the bars show the amount ABOVE 95 rather than the values themselves, and a 10% difference is drawn as though it were threefold
• The values must have been plotted incorrectly
• Nothing is wrong; starting an axis higher up saves space
• The bars need labels on top

Honest and misleading

The same data set, drawn two ways. Everything in the right-hand column is a choice somebody made.

When a picture doubles

A pictogram uses a picture of a house to represent house sales. Sales have doubled, so the designer draws the second house twice as tall AND twice as wide. Select the TWO correct criticisms.

• The second picture has four times the area of the first, so it looks like a fourfold increase rather than a twofold one
• Only one number is being shown, so only one dimension should change, or identical symbols should be repeated instead
• It is acceptable because the picture is still in proportion
• The problem is that the two houses are different colours

The histogram version of the trick

Everything above applies to any chart. This one is specific to histograms, and it is marked **Higher only** on the specification. **On a histogram the AREA of a bar is the frequency, not its height.** That is why the vertical axis has to be frequency density whenever the class widths differ. **The misrepresentation is to plot frequency as height anyway.** Suppose one class is 20 wide holding 40 values and the next is 5 wide holding 30. Plotted as frequency density they are 2 and 6, and the first bar covers the greater area because it is four times wider. **Plotted as raw frequency, the first bar is drawn taller than the second and a reader comparing heights reaches the opposite conclusion about which class is larger.** **Notice this is the same fault as all the others.** The eye is reading a height, and on a histogram height is not the quantity. Get the axis wrong and the link between the number and what your eye measures is broken, exactly as a truncated axis breaks it on a bar chart.

Reading a chart critically

A vertical axis that does not start at _____ is described as _____, and its effect is to make small differences look large. Scaling a picture in both height and width to show one number is called _____, and doubling both dimensions gives _____ times the area. On a histogram with unequal class widths, plotting _____ as the height instead of frequency density misleads because on a histogram the _____ of a bar represents the frequency.

How much bigger does it look?

A pictogram symbol is scaled up so that its height and its width are both **three times** the original. By what factor has its AREA increased?

Critiquing a graphic

**"A newspaper prints a bar chart of a company's profits for three years. Comment on how it has been presented. (6 marks)"** "**The vertical axis is truncated**, starting at 40 rather than zero. The profits rose from 42 to 48, an increase of about 14%, but because only the amount above 40 is drawn, the final bar appears roughly four times the height of the first. **The effect on the reader** is to suggest a dramatic rise where the data shows a modest one. A reader who does not check the axis, which is most readers, takes the impression rather than the numbers. **The chart is also drawn with a three-dimensional effect**, which makes the front bar look larger than an equal bar behind it, so position on the chart affects apparent size. **How it should be redrawn**: a vertical axis starting at zero, drawn flat rather than in perspective. The rise would still be visible and would be shown at its actual size." **Three things that answer does, and the third is what most miss.** It **names the technique**. It **quantifies the distortion** - 14% shown as fourfold - rather than saying the chart is misleading. And it **says how the chart should be redrawn**, which turns a criticism into a correction and is usually worth the final mark.

Spot the two problems

A description of an infographic. Tap the TWO details that describe a graphical misrepresentation.

• The infographic uses a clear colour scheme and both axes carry units.
• The vertical axis begins at 80 rather than at zero, although the values plotted range only from 82 to 91
• A key explains what each shade means.
• Where a figure has doubled, the symbol beside it is drawn at double the height and double the width
• The source of the data is given underneath.

Write the criticism

Build a criticism that does all three jobs: name it, quantify it, and correct it.

A graphic in the news

You are asked to critique a chart published in a newspaper. Work through it.

• What do you check first, before reading anything else on the chart?
• The chart shows only the last three months of a five-year series. Is that a problem?
• You have identified two problems. How do you finish the answer?

Your turn: critique and correct

A chart shows sales of 210, 225 and 240 units over three years. Its vertical axis begins at 200, it is drawn in three dimensions, and each year is marked with a symbol scaled in both directions. Critique it.

• Name each technique used, using the specification's own terms
• For the truncated axis, quantify the distortion: state the real percentage increase and describe how large it is made to appear
• Explain why scaling a symbol in two directions overstates a single number, giving the factor
• Describe how the chart should be redrawn so that it presents the same data honestly