Comparing data sets | Year 9

01 / LEARN

The idea, step by step

Compare like with like

Check that the groups measure the same variable in the same units under comparable conditions. Sort small lists, then calculate a measure of centre and a measure of spread. The mean uses every value; the median is the middle ordered value. The range is maximum minus minimum.

Context determines what counts as favourable: a shorter waiting time may be desirable, while a higher score may be desirable. The highest observation alone does not describe a typical member of the group.

Both groups use the same measurement units.
Group A	Group B
10	11
12	12
12	13
14	14
17	15

Use evidence without overclaiming

A good comparison joins the context to the numbers: Group A has a lower median wait, but Group B has a smaller range. Equal means do not imply equal distributions. If the groups overlap, do not claim that every value in one group is better.

Mention important limitations, including small samples, selection method and different conditions. A descriptive comparison does not prove that membership of a group caused a difference.

A common trap

A larger mean means every value in that group is larger.

Instead: Inspect overlap and spread; a summary does not describe every individual value.

02 / WORKED EXAMPLES

See the thinking

Example 1

Equal means, different spread

Compare A: 10, 12, 12, 14, 17 and B: 11, 12, 13, 14, 15.

Both groups use the same measurement units.
Group A	Group B
10	11
12	12
12	13
14	14
17	15

Both totals are 65, so both means are $65 / 5 = 13$ .
The medians are 12 and 13. Ranges are $17 - 10 = 7$ and $15 - 11 = 4$ .
B has the smaller range; A has the lower median. The groups overlap.

Both means 13; A median 12/range 7; B median 13/range 4.

Example 2

Compare delivery times

Times in minutes: A: 18, 20, 20, 22, 25; B: 15, 19, 21, 23, 27.

Each total is 105, giving mean 21.
A has median 20 and range 7. B has median 21 and range 12.
A has a slightly shorter median and more consistent sample times; this does not mean every A delivery is faster.

A has the lower sample median and smaller range.

Check your understanding

A has median 12/range 9. B has median 12/range 4. Compare them.

Show answer

Equal medians; B is less spread out by range.

The centre is the same, but the distributions need not be identical.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find mean, median and range for 3, 5, 5, 7, 10.
3 marks
A: 6, 7, 8, 9, 10. B: 4, 8, 8, 8, 12. Compare means and ranges.
3 marks
A: 11, 12, 13. B: 10, 14, 15. Does B's higher mean show every B score is higher?
2 marks
Two waiting-time samples have medians 8 and 11 minutes. Interpret the difference.
2 marks
Why is comparing raw totals from a five-minute test with a ten-minute test unfair?
2 marks
A sample of six has a higher median score than another sample of six. Write a cautious conclusion.
2 marks

Read the worked solutions

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

Find mean, median and range for 3, 5, 5, 7, 10.
3 marks
Total is 30, so mean $= 30 / 5 = 6$ .
The middle is 5; $10 - 3 = 7$ .
Mean 6; median 5; range 7.
A: 6, 7, 8, 9, 10. B: 4, 8, 8, 8, 12. Compare means and ranges.
3 marks
Both totals are 40.
$10 - 6 = 4$ and $12 - 4 = 8$ , so A is less spread out.
Both means 8; A range 4, B range 8.
A: 11, 12, 13. B: 10, 14, 15. Does B's higher mean show every B score is higher?
2 marks
A mean is 12 and B mean is 13.
A group mean does not imply a claim about all individuals.
No; B contains 10, below every A score.
Two waiting-time samples have medians 8 and 11 minutes. Interpret the difference.
2 marks
$11 - 8 = 3$ minutes.
It does not mean each individual wait differs by 3 minutes.
The first sample's middle waiting time is 3 minutes shorter.
Why is comparing raw totals from a five-minute test with a ten-minute test unfair?
2 marks
The longer test allows more events.
Use the same conditions or a suitable rate, explaining remaining differences.
The groups have different amounts of time or opportunity.
A sample of six has a higher median score than another sample of six. Write a cautious conclusion.
2 marks
This evidence describes two small samples.
Sampling variation or other differences may explain the result.
The first sample has a higher median; larger fair samples are needed before generalising.

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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 ↗

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