Misleading graphs and representations | Year 9

01 / LEARN

The idea, step by step

Read the scale before the shape

A bar-height difference can look dramatic when the vertical axis starts above zero. A nonzero scale is not automatically dishonest, but the baseline must be clear and numerical comparisons must use actual values. A larger-looking picture can also exaggerate a change when both height and width are increased.

Check units, equal numerical intervals, omitted dates and sample sizes. A graph across time should place times at their true intervals. A steep-looking segment means little until you read the horizontal and vertical scales.

Use the right denominator

Counts tell how many events occurred; rates relate them to the number of opportunities. Twelve complaints from 300 orders is 4%, while ten from 200 is 5%. The business with more raw complaints may have the lower complaint rate.

Also check causal language. Two quantities changing together does not establish that one causes the other. A responsible conclusion identifies what was actually observed and leaves room for other explanations.

Business	Complaints	Orders	Rate
A	12	300	4%
B	10	200	5%

A common trap

The largest-looking bar proves the largest proportional change.

Instead: Read the numbers and baseline rather than relying on the visual dimensions.

02 / WORKED EXAMPLES

See the thinking

Example 1

An exaggerated sales claim

The graph shows 48 bottles on Monday and 52 on Tuesday. A caption says sales more than doubled.

Actual increase $= 52 - 48 = 4$ .
$52 / 48 \approx 1.083$ , not more than 2.
The truncated baseline exaggerates relative bar heights; the real increase is about 8.3%.

The claim is false: 4 more bottles, about 8.3%.

Example 2

Counts versus rates

A has 12 complaints from 300 orders; B has 10 from 200. Which complaint rate is lower?

A: $12 / 300 = 4 %$ .
B: $10 / 200 = 5 %$ .
A has the lower rate despite its larger raw count.

A, with 4% rather than 5%.

Check your understanding

A score rises from 50 to 55. Is that a 5% increase?

Show answer

No; it is 10%.

The increase is 5 out of the original 50: $5 / 50 \times 100 = 10 %$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Attendance rises from 120 to 132. Find the numerical and percentage increases.
3 marks
A poll reports 80% agreement without giving a sample size. Name two missing details that matter.
2 marks
A has 8 late appointments out of 100; B has 12 out of 200. Compare late rates.
2 marks
A graph places years 2010, 2011 and 2020 equally far apart. Explain the issue.
2 marks
An icon doubles in both height and width. By what factor does its area change, and why can this mislead?
2 marks
Ice-cream sales and swimming incidents both rise in hot weather. Does this prove ice cream causes incidents?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Attendance rises from 120 to 132. Find the numerical and percentage increases.
3 marks
Increase $= 12$ .
$12 / 120 \times 100 = 10 %$ .
12 people; 10%.
A poll reports 80% agreement without giving a sample size. Name two missing details that matter.
2 marks
80% of 5 has different stability from 80% of 5,000.
Voluntary or biased selection may distort the proportion.
Sample size and selection method.
A has 8 late appointments out of 100; B has 12 out of 200. Compare late rates.
2 marks
$8 / 100 = 8 %$ .
$12 / 200 = 6 %$ .
A: 8%; B: 6%; B is lower.
A graph places years 2010, 2011 and 2020 equally far apart. Explain the issue.
2 marks
Equal horizontal distances should mean equal times when showing change.
Use proportional spacing or a different clearly explained display.
A nine-year interval is drawn the same width as a one-year interval.
An icon doubles in both height and width. By what factor does its area change, and why can this mislead?
2 marks
Area factor $= 2 \times 2 = 4$ .
Viewers may infer four times the quantity when only doubling was intended.
Area becomes four times as large.
Ice-cream sales and swimming incidents both rise in hot weather. Does this prove ice cream causes incidents?
2 marks
The evidence shows an association.
Other explanations and appropriate study evidence are needed for causation.
No; hot weather may influence both.

Checking saved progress…

Continue learning

Choosing a display for the data

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 9 sampling, comparative distributions, centre/spread/outliers, displays, critique and statistical investigations.

Official curriculum source ↗

Back to Statistics