Spotting misleading graphs Revision Card

AI generatedStatisticsKey Stage 3

Spotting misleading graphs.

Check the starting value and spacing of the scale before comparing heights.
Frequency bar charts should have a zero baseline, equal bar widths and a consistent scale.
Explain the distortion using the actual values, then state a correction.

Example 1

The bars make B look three times as large as A. Explain why this is misleading.

The vertical axis starts at 40, so the drawn heights show 2 and 6 rather than the full frequencies 42 and 46. Start a frequency bar chart at zero. B is only 4 greater than A.

Example 2

The vertical labels increase by 10, 10, 30 and 10 over equal spaces. Explain the problem.

Equal vertical distances represent different changes. Use one constant scale so equal steps represent equal increases.

Your turn

Question 1

Bar B is wider as well as taller. Explain why the display is misleading.

Check answer

For a bar chart, compare frequencies using height on a common scale. Unequal widths exaggerate the area of B; use equal-width bars.

Question 2

Someone says B has three times the frequency of A. Use the scale to check.

Check answer

False. The frequencies are 62 and 66, only 4 apart. Starting at 60 exaggerates the visible height ratio; draw the bars from zero.

Question 3

Suggest one improvement to make the categories fair to compare.

Check answer

Use equal-width bars with gaps between categories. Keep the same frequency scale for both bars.

Question 4

Can you read 35 by going halfway between the 20 and 50 labels on this scale? Explain the issue.

Check answer

That would use a different rate from the rest of the axis. Redraw with equal numerical intervals at equal distances before interpreting bar heights.

Question 5

The graph claims a very large increase from A to B. State the actual increase and improve the graph.

Check answer

The increase is

. Begin the frequency axis at zero so the visible bar heights show the full frequencies.