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hscscience Maths Std · Y11
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Module 4 · L2 of 6 ~20 min MS-S1 ⚡ +90 XP available

Collecting Data

A bad sample ruins good analysis. It does not matter how sophisticated your calculations are if your data comes from a biased source. This lesson teaches you how to collect data properly: census versus sample, random versus stratified sampling, and the many forms of bias that can creep into your data.

Today's hook, You want to find the average amount of pocket money for teenagers in Australia. Would you ask only students at your school? Why or why not?
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Recall, your gut answer first

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Recall, your gut answer first
+5 XP warm-up

You want to find the average amount of pocket money for teenagers in Australia. Would you ask only students at your school? Why or why not?

Without looking ahead write your gut feeling. We'll revisit this at the end of the lesson.

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02
The key principles you need to own
+5 XP to read

Good statistical conclusions depend on representative data collection. A biased sample produces misleading results no matter how correct the subsequent calculations are.

Census
Data from every member of a population. Most accurate but expensive and time-consuming.
Sample
Data from a selected subset. Faster and cheaper, but may not represent the whole population.
Bias
A systematic error that causes results to consistently favour one outcome. Quality beats quantity.
Key insight: A representative sample is more valuable than a large biased sample. Quality of sampling beats quantity.
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What you'll master
Know

Key facts

  • The difference between census and sample
  • Types of sampling methods
  • Types of bias in data collection
Understand

Concepts

  • Why samples can be biased
  • How to reduce bias in sampling
  • When a census is necessary
Can do

Skills

  • Design an appropriate sampling method
  • Identify and name sources of bias
  • Calculate stratified sample sizes
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Key terms
CensusData collected from every single member of a population. Example: Australian Census every 5 years.
SampleA selected subset of the population from which data is collected.
Random sampleEvery member of the population has an equal chance of being selected.
Stratified samplePopulation divided into groups (strata), then randomly sampled from each group in proportion.
BiasA systematic error that causes data to consistently favour one outcome over others.
Selection biasSome groups are systematically excluded or under-represented in the sample.
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Census vs sample, who should you ask?

Census: Collects data from every single member of a population.

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Census vs sample, who should you ask?
core concept

Census: Collects data from every single member of a population.

  • Advantages: most accurate, complete picture
  • Disadvantages: expensive, time-consuming, often impractical

Sample: Collects data from a selected subset.

  • Advantages: faster, cheaper, practical for large populations
  • Disadvantages: may not represent the whole population

The Australian Census happens every 5 years and attempts to count every person. Most research, however, uses samples.

Sampling methods: Simple random (equal chance), Stratified (proportional groups), Systematic (every nth person), Convenience (whoever is nearby, often biased), Self-selected (volunteers, attracts strong opinions).

Census collects data from every member of a population, accurate but expensive and time-consuming. A sample surveys a subset and is cheaper and faster but risks being unrepresentative if not selected carefully.

Pause, copy the census vs sample trade-off (census: accurate but costly; sample: fast but risks bias) and the two conditions a good sample must meet (representative and large enough) into your book.

Quick check: A school with 40% Year 7, 35% Year 8, and 25% Year 9 wants a sample of 80. How many Year 7 students should be selected in a stratified sample?

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Types of bias, when samples go wrong

We just saw that a census measures every member of the population while a sample measures a subset, and that a sample is...

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Types of bias, when samples go wrong
core concept

We just saw that a census measures every member of the population while a sample measures a subset, and that a sample is cheaper but risks being unrepresentative. That raises a question: even when we take a sample, what specific things can go wrong that make it give misleading results? This card answers it → three types of bias, selection bias, response bias, and voluntary response bias, each systematically distorts results in a predictable direction.

Bias is a systematic error that distorts your results in a consistent direction.

Selection bias
Some groups are systematically excluded. A phone survey about internet usage excludes people without phones.
Response bias
Questions are leading, or people give socially desirable answers rather than honest ones.
Non-response bias
Those who do not respond differ systematically from those who do. Email surveys with low return rates suffer from this.

Self-selection bias: When people voluntarily participate, those with strong opinions are over-represented (e.g., TV call-in votes).

Bias systematically distorts results in one direction. Key types: selection bias (some groups excluded), response bias (wording or presence of interviewer affects answers), voluntary response bias (self-selected participants skew results).

Pause, copy the three bias types with one example each: selection bias (some groups excluded from sampling), response bias (question wording or interviewer affects answers), and voluntary response bias (self-selected respondents skew toward strong opinions) into your book.

True or false: A TV station asking viewers to call in and vote is an example of selection bias because only motivated viewers call.

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Worked example · stratified sampling

Worked example · stratified sampling

Worked example · stratified sampling

PROBLEM 1 · STRATIFIED SAMPLING

A school has 500 Year 11 students: 300 female, 200 male. A researcher wants to survey 50 students about homework time. Describe a stratified sampling method and explain why it is better than convenience sampling.

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Calculate proportions
Female: 300/500 = 60% · Male: 200/500 = 40%
Stratified sampling means each group is sampled in proportion to its size in the population.
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Fill the gap: A city has 60% adults and 40% teenagers. For a stratified sample of 100, you would select adults and teenagers.

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Quick-fire practice · identify bias

Quick-fire practice · identify bias

Quick-fire practice · identify bias

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A weight loss study only includes volunteers who are already trying to lose weight. What type of bias?

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A teacher surveys only the front row about classroom temperature. What type of bias?

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A company emails 10,000 customers and gets 200 responses. Name at least two sources of bias.

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Why might a random sample still be biased even if selection was truly random?

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A school has 200 Year 10 and 300 Year 11 students. In a stratified sample of 100, how many from each year?

Match each scenario to its bias type:

  • Phone survey excludes those without phones
  • Survey asks leading questions
  • Only satisfied customers reply to email survey
  • Volunteers with strong opinions call in
  • Non-response bias
  • Self-selection bias
  • Selection bias
  • Response bias

Top 3 list: Name THREE advantages of using a stratified sample over a simple random sample.

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Revisit your thinking

Look back at what you wrote in the Think First section.

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Revisit your thinking

Look back at what you wrote in the Think First section. Asking only your school would create selection bias, your school may have different socioeconomic status, location, or culture than the national average. A better approach: stratified random sampling across multiple school types and locations. Even then, self-reporting may introduce response bias as students may exaggerate or underreport.

What did you get right? What surprised you?

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Show what you have learned

Multiple choice, then short answer under exam conditions.

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Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next.

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Short answer
ApplyBand 42 marks

SA 1. A company wants to survey customer satisfaction. They send an email to 10,000 customers and receive 200 responses. (a) What type of sample is this? (b) Identify at least two sources of bias. (c) Suggest a better sampling method. (2 marks)

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AnalyseBand 53 marks

SA 2. (a) Explain why the Australian Census attempts to count every person rather than using a sample. (b) A researcher studies drug use among teenagers by standing outside a nightclub on Saturday night. Identify all forms of bias. (c) Design a better sampling strategy for this sensitive topic, explaining your choices. (3 marks)

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📖 Comprehensive answers (click to reveal)

Drill 1: Selection/self-selection bias, only motivated participants volunteer. 2: Convenience bias, front row may differ from back row. 3: Non-response bias (only motivated customers reply) + selection bias (only email-accessible customers). 4: Non-response bias still possible; chance alone may over-represent one group. 5: Year 10: 40, Year 11: 60.

SA 1 (2 marks): (a) Self-selected (voluntary response) sample [0.5]. (b) Non-response bias, only satisfied/dissatisfied customers respond; selection bias, only email users included [0.5]. (c) Random sample with follow-up, or stratified by customer type [1].

SA 2 (3 marks): (a) Census provides complete data for government planning and funding, some data must be exact [1]. (b) Selection bias (nightclub-goers only), time bias (Saturday night only), response bias (may lie about illegal activity), self-selection [1]. (c) Anonymous online/paper survey through schools, stratified by school type and location, anonymity reduces response bias [1].