Sampling and survey quality | Year 9

01 / LEARN

The idea, step by step

Start with the population

A population is the full group named in your question. A sample is the smaller group actually measured. Write the population precisely: all Year 9 students is different from your own class. The sampling frame is the list or access method used to reach them. A random choice from an incomplete list can still miss important people.

Random sampling uses chance to choose from a suitable frame. Systematic sampling uses a random start and a fixed interval. Stratified sampling divides the population into relevant groups and samples within each group. These methods improve coverage; they do not guarantee a particular result.

Look for missing voices

Convenience samples include whoever is easiest to reach. Voluntary polls include whoever chooses to reply. Both can over-represent people with particular interests. Leading wording may affect responses too. Use a neutral question and record how many selected people did not answer.

A larger sample generally reduces chance variation, but does not repair biased selection. Surveying 500 keen footballers is still a poor way to estimate the views of all students about sports spending. Explain the source of bias rather than simply calling a sample unfair.

A proportional sample of 30 from 400 students
Year	Students	Sample
7	200	15
8	120	9
9	80	6

A common trap

A big sample must be representative.

Instead: Size helps with chance variation; it cannot repair the exclusion of important groups.

02 / WORKED EXAMPLES

See the thinking

Example 1

A convenient sample

Students leaving football practice are asked whether the school needs more sports equipment. Can the result represent all students?

The intended population includes students who do not play football.
The selected group may place more value on sports equipment.
Randomly sample from the full school roll, possibly within each year group.

Not reliably. The sample is likely to over-represent students interested in sport.

Example 2

A proportional sample

A school has 200 Year 7, 120 Year 8 and 80 Year 9 students. Allocate a sample of 30.

Total population is 400.
Year 7: $200 / 400 \times 30 = 15$ ; Year 8: $120 / 400 \times 30 = 9$ .
Year 9: $80 / 400 \times 30 = 6$ . Check the three counts total 30, then randomly select within each group.

15 Year 7, 9 Year 8 and 6 Year 9 students.

Check your understanding

Names are randomly drawn from a list containing only students who own a phone. Is this a fair frame for all students?

Show answer

Not reliably.

Students without phones cannot be selected, even though the draw from this incomplete list is random.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

A principal surveys 60 of the school's 900 students. Name the population and sample.
2 marks
A gardening-club poll estimates how many town residents grow vegetables. Explain one likely bias.
2 marks
A year group has 180 students in A and 120 in B. Allocate a proportional sample of 50.
3 marks
Explain how to choose a systematic sample of 10 from a list of 100, using a random start.
2 marks
Rewrite neutrally: Do you agree that our excellent new canteen is much better?
2 marks
Forty names are chosen randomly, but only 18 students reply. Why should a report mention this?
2 marks

Read the worked solutions

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

A principal surveys 60 of the school's 900 students. Name the population and sample.
2 marks
The target is the whole school.
Only 60 students supply responses.
Population: all 900 students. Sample: the 60 surveyed.
A gardening-club poll estimates how many town residents grow vegetables. Explain one likely bias.
2 marks
The frame is club users, not all residents.
Interest in gardening is linked to the question.
Gardeners are more likely to see and answer it, so the estimate may be high.
A year group has 180 students in A and 120 in B. Allocate a proportional sample of 50.
3 marks
Total is 300.
$180 / 300 \times 50 = 30$ and $120 / 300 \times 50 = 20$ .
30 from A; 20 from B.
Explain how to choose a systematic sample of 10 from a list of 100, using a random start.
2 marks
The interval is $100 / 10 = 10$ .
The random start avoids always choosing the same initial position.
Randomly select a position from 1 to 10, then take every tenth name.
Rewrite neutrally: Do you agree that our excellent new canteen is much better?
2 marks
Remove praise and the suggested answer.
Offer better, about the same, worse and unsure as balanced choices.
How would you rate the new canteen compared with the previous canteen?
Forty names are chosen randomly, but only 18 students reply. Why should a report mention this?
2 marks
Only $18 / 40 = 45 %$ replied.
Random selection does not guarantee representative completed responses.
Non-response may bias the results if respondents differ from non-respondents.

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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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