A firm says the bar chart below shows this year's orders (hundreds) are several times last year's: A is last year, B this year. What is misleading about it? A. Nothing is misleading B. The bars have different widths C. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values D. It should have been a line graph Choose the right answer

C. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values. Starting at 50, the bars are only 54 − 50 and 68 − 50 high, stretching the gap; really 68 is just 68 − 54 more than 54.

A drinks shop's poster compares two drinks' sales in a day (cups) on a bar chart whose vertical axis starts at 80. Drink A sold 86 cups, and bar B looks 1.5 times as tall as bar A. How many cups did drink B really sell?

89 cups. The bars start at 80: bar A is 86 − 80 = 6 high, bar B 1.5 × 6 = 9, so B = 80 + 9 = 89 cups, short of 1.5 times A.

Cumulative frequency & charts · Ages 14–15

Misleading statistical charts

First check whether the vertical axis starts at 0.

How to do it

Method

First check whether the vertical axis starts at 0

Axis from 50: 52 and 56 give bars 2 and 6 high

Another way

Compare the ratios

Looks 6 ÷ 2 = 3 times; really 56 ÷ 52 ≈ 1.08 times

In full

Look at the scale first. If the vertical axis doesn't start at 0, the bars' heights are no longer in proportion to the values: values 52 and 56 on an axis starting at 50 give bars 2 and 6 high, which look 3 times apart, though 56 is only about 8% more than 52. One check: read off the true values and compare them (56 − 52 = 4, 4 ÷ 52 × 100% ≈ 7.7%). Another: measure how many times taller one bar looks (6 ÷ 2 = 3) and set it beside the true ratio (56 ÷ 52); if they differ, the chart misleads. Other common misuses: an uneven scale; a picture made both longer and wider, so its area grows as the square of the ratio (2 times each way is 4 times the area); a pie chart whose percentages don't add up to 100%.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
The bar chart compares two phones' battery capacities (hundreds of mAh), its vertical axis starting at 40. How many times as tall as bar A does bar B look?
Show the answer and working
Answer: 2 times
Starting at 40, bar A is 46 − 40 high and bar B 52 − 40: 2 times as tall, though 52 ÷ 46 is far less than 2.
Example 2
A firm says the bar chart below shows this year's orders (hundreds) are several times last year's: A is last year, B this year. What is misleading about it?
- A. Nothing is misleading
- B. The bars have different widths
- C. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
- D. It should have been a line graph
Choose the right answer
Show the answer and working
Answer: C. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
Starting at 50, the bars are only 54 − 50 and 68 − 50 high, stretching the gap; really 68 is just 68 − 54 more than 54.
Example 3
A drinks shop's poster compares two drinks' sales in a day (cups) on a bar chart whose vertical axis starts at 80. Drink A sold 86 cups, and bar B looks 1.5 times as tall as bar A. How many cups did drink B really sell?
Show the answer and working
Answer: 89 cups
The bars start at 80: bar A is 86 − 80 = 6 high, bar B 1.5 × 6 = 9, so B = 80 + 9 = 89 cups, short of 1.5 times A.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.The bar chart compares two phones' battery capacities (hundreds of mAh), its vertical axis starting at 50. How many times as tall as bar A does bar B look?
Answer:
2.In the bar chart below, the vertical axis starts at 40. Bar B is 3 times as tall as bar A, so B's value is 3 times A's too.
True or false?
Answer:
3.The bar chart shows how many tubs of ice cream two branches sold in a week, its vertical axis starting at 80. Branch A sold tubs and branch B .
Fill in each blank
Answer:
4.A firm says the bar chart below shows this year's orders (hundreds) are several times last year's: A is last year, B this year. What is misleading about it?
- A. It should have been a line graph
- B. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
- C. Nothing is misleading
- D. The bars have different widths
Choose the right answer
Answer:
5.Tsz-ching's poster shows savings as a picture of a money bag. This year's savings are 4 times last year's, and the bag is drawn 4 times as long and 4 times as wide. How many times as large is this year's bag's area?
Answer:

All the answers

1. 2 times
2. False
3. 82, 88
4. B. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
5. 16 times

Free worksheet: Misleading statistical chartsWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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