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A school studies all 100k students but measures everyone’s height with a ruler biased by +1 cm. Is there sampling error? Is there measurement bias?

Read the idea, work independently, then explain what changed.

TOPIC 01

Statistics: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

A school studies all 100k students but measures everyone’s height with a ruler biased by +1 cm. Is there sampling error? Is there measurement bias?

k=9k=9
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Identify the population and sampling mechanism before scaling counts.
Hint 2
Separate coverage from how the measurement was obtained.
Worked solution
  1. Identify the population and sampling mechanism before scaling counts.

  2. Calculate or simplify this relation.

    census≠error-free measurement\text{census}\ne\text{error-free measurement}
  3. A census does not remove measurement, processing or nonresponse problems.

No sampling error from selection; yes, a systematic measurement bias remains.

Checks and common pitfalls: A census does not remove measurement, processing or nonresponse problems.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗