GRAPHS AND STATISTICS

Misleading Data

Learn the reliable method for misleading data, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A graph can mislead when its scale, intervals or visual areas distort the numerical comparison.

Picture itRead the scale before the bars
2 · THE METHOD

Follow these steps

  1. Check where each axis begins.
  2. Check that equal visual gaps represent equal numerical intervals.
  3. Compare the data values rather than the apparent size of bars or symbols.
3 · WORKED EXAMPLES

See the method in action

Example 1

A chart of tickets sold uses equally spaced vertical labels 0, 10, 30, 40. Which change makes this scale consistent?

  1. Equal distances on a linear axis must represent equal numerical intervals.
  2. The corrected labels 0, 10, 20, 30 increase by 10 each time.
Answer: Change 30 to 20 and 40 to 30.
Example 2

Two bars show 57 and 62 tickets sold. Their vertical axis starts at 52. The second bar looks twice as tall. Which statement correctly compares the actual totals?

  1. The drawn heights represent 57 − 52 = 5 and 62 − 52 = 10.
  2. But the actual difference is 62 − 57 = 5; starting the axis above zero exaggerates the ratio.
Answer: The second total is 5 greater, not twice the first.
4 · ELEVENSPRINT TIP

A useful shortcut

Compare the data values rather than the apparent size of bars or symbols.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.