Australian Curriculum v9 / ACiQ Year 10 Mathematics - Unit 4 - Statistical claims, bias and ethics

Statistical claims, bias and ethics

Evaluate statistical claims by examining sampling, representation, variability, causation, ethics and stakeholder impact.

Updated 2026-07-26 - 12 min read

Statistical claims, bias and ethics is taught here as a connected set of decisions, not a list of facts. Work through the prerequisite recall, explicit models, carefully faded examples, misconception repairs and transfer task before using the target in Check, Practice, Review or Rapid Revision.

This note is designed to work with the guided lessons, curated practice, flashcards, Tutor context, Review and Rapid Revision for the same canonical target. The same three evidence checks are used throughout, so feedback can route a learner back to the precise idea that needs repair.

Audit sampling and measurement

Judge whether the sampling frame, selection process and measurement method represent the target population and variable. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by audit sampling and measurement and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Increasing size reduces random variation but does not remove systematic exclusion or leading measurement.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 1.1

A poll of 50,000 app users estimates all adults' views. What is a key concern?

Step 1 - identify the governing idea: Judge whether the sampling frame, selection process and measurement method represent the target population and variable.

Step 2 - apply it to this evidence: App users and volunteers may differ from the target population.

Result: Coverage and self-selection bias

The relationship is visible in the working: App users and volunteers may differ from the target population. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • The sample is too small — It does not agree with the required relationship: App users and volunteers may differ from the target population.
  • Percentages cannot be used — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Large samples have no uncertainty — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.2

Which survey wording is least leading?

Step 1 - identify the governing idea: Judge whether the sampling frame, selection process and measurement method represent the target population and variable.

Step 2 - apply it to this evidence: It requests a measurable value without signalling a preferred response.

Result: How many hours did you study last week?

The relationship is visible in the working: It requests a measurable value without signalling a preferred response. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Don't you study enough? — It does not agree with the required relationship: It requests a measurable value without signalling a preferred response.
  • Why are students lazy? — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Surely tutoring helps, right? — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.3

A scale consistently reads 0.8 kg high. What type of problem is this?

Step 1 - identify the governing idea: Judge whether the sampling frame, selection process and measurement method represent the target population and variable.

Step 2 - apply it to this evidence: The error shifts measurements in the same direction.

Result: Systematic measurement bias

The relationship is visible in the working: The error shifts measurements in the same direction. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Random sampling variation — It does not agree with the required relationship: The error shifts measurements in the same direction.
  • A larger population — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • No error — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Evaluate claims and data displays

Check denominators, axes, omitted groups, summary choices and whether the evidence supports association or causation. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by evaluate claims and data displays and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Scale, truncation and selection can distort visual interpretation without changing individual data values.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 2.1

A bar chart axis begins at 95 and differences look huge. What should be checked?

Step 1 - identify the governing idea: Check denominators, axes, omitted groups, summary choices and whether the evidence supports association or causation.

Step 2 - apply it to this evidence: Bar lengths normally encode magnitude from a meaningful baseline.

Result: The truncated scale exaggerates visual differences

The relationship is visible in the working: Bar lengths normally encode magnitude from a meaningful baseline. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • The data must be false — It does not agree with the required relationship: Bar lengths normally encode magnitude from a meaningful baseline.
  • Bars should be circular — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • The sample is necessarily random — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.2

Ice-cream sales and sunburn both rise in summer. What is a plausible explanation?

Step 1 - identify the governing idea: Check denominators, axes, omitted groups, summary choices and whether the evidence supports association or causation.

Step 2 - apply it to this evidence: A third variable influences both observed quantities.

Result: Temperature is a confounding variable

The relationship is visible in the working: A third variable influences both observed quantities. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Ice cream causes sunburn — It does not agree with the required relationship: A third variable influences both observed quantities.
  • Sunburn causes ice-cream sales — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Correlation proves both — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.3

A claim reports 'risk doubled' from 1 in 10,000 to 2 in 10,000. What context is important?

Step 1 - identify the governing idea: Check denominators, axes, omitted groups, summary choices and whether the evidence supports association or causation.

Step 2 - apply it to this evidence: Relative and absolute changes communicate different practical sizes.

Result: The absolute increase is 1 in 10,000

The relationship is visible in the working: Relative and absolute changes communicate different practical sizes. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • The risk became certain — It does not agree with the required relationship: Relative and absolute changes communicate different practical sizes.
  • The increase is 100 percentage points — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • No denominator is needed — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Reason ethically with data

Minimise unnecessary data collection, protect privacy, report uncertainty and consider who may be harmed by categories or decisions. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by reason ethically with data and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Purpose limitation and data minimisation reduce privacy and misuse risks.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 3.1

Which practice best follows data minimisation?

Step 1 - identify the governing idea: Minimise unnecessary data collection, protect privacy, report uncertainty and consider who may be harmed by categories or decisions.

Step 2 - apply it to this evidence: Unnecessary personal fields increase risk without supporting the analysis.

Result: Collect only variables needed for the stated question

The relationship is visible in the working: Unnecessary personal fields increase risk without supporting the analysis. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Collect all identifiers — It does not agree with the required relationship: Unnecessary personal fields increase risk without supporting the analysis.
  • Publish raw responses — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Retain data forever — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.2

Why can publishing a tiny subgroup's results be risky?

Step 1 - identify the governing idea: Minimise unnecessary data collection, protect privacy, report uncertainty and consider who may be harmed by categories or decisions.

Step 2 - apply it to this evidence: Small cells can reveal sensitive information even without names.

Result: Individuals may be re-identifiable

The relationship is visible in the working: Small cells can reveal sensitive information even without names. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Means cannot be calculated — It does not agree with the required relationship: Small cells can reveal sensitive information even without names.
  • Subgroups are always biased — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Ethics apply only to experiments — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.3

A model performs worse for one demographic group. What should be done?

Step 1 - identify the governing idea: Minimise unnecessary data collection, protect privacy, report uncertainty and consider who may be harmed by categories or decisions.

Step 2 - apply it to this evidence: Aggregate accuracy can conceal unequal harms.

Result: Investigate data, error rates and impacts before deployment

The relationship is visible in the working: Aggregate accuracy can conceal unequal harms. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Ignore the subgroup — It does not agree with the required relationship: Aggregate accuracy can conceal unequal harms.
  • Delete the group — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Report only overall accuracy — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Retrieval check

Try these without looking back at the examples.

  1. Which survey wording is least leading?
  2. Ice-cream sales and sunburn both rise in summer. What is a plausible explanation?
  3. Why can publishing a tiny subgroup's results be risky?

Answers

  1. How many hours did you study last week? — It requests a measurable value without signalling a preferred response.
  2. Temperature is a confounding variable — A third variable influences both observed quantities.
  3. Individuals may be re-identifiable — Small cells can reveal sensitive information even without names.

Transfer task

Find an unfamiliar example from school, daily life, a credible news source or another subject. Explain which of the three evidence checks applies. Complete the task, then audit your own response: identify the evidence used, the relationship applied, one plausible misconception and the final reasonableness check. If a peer could not reproduce your reasoning, add the missing step.

Sources