LEARN · EXPLAIN · REVISE

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.

高一必修第二册(A版).pdf · 9.1 · PDF 180 / printed page 173

TOPIC 01

Random sampling

Build understanding of random sampling through definitions, contrasting cases and justified applications.

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

01 / Transfer#Worked example

k=2

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

Identify the population and sampling mechanism before scaling counts.
Calculate or simplify this relation.
$\text{census}\ne\text{error-free measurement}$
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

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

Teacher preparation and assessment

Use random sampling to state a justified conclusion.
Sampling design: Simple random, systematic and stratified procedures define how units are selected.
Error sources: Coverage, nonresponse and measurement problems differ from random sampling variation.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Simple random, systematic and stratified procedures define how units are selected.
Expected reasoning: Coverage, nonresponse and measurement problems differ from random sampling variation.
Expected correction: A larger sample does not automatically remove selection bias.