LEARN · EXPLAIN · REVISE

Two strata have mean commute times 20 and 40 minutes and sizes 3k and k. Find the overall mean.

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

高一必修第二册(A版).pdf · 9.3 · PDF 227 / printed page 220

TOPIC 01

Statistical case study

Build understanding of statistical case study through definitions, contrasting cases and justified applications.

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

01 / Standard#Worked example

k=2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

State the survey question, population, sampling and measurement rules before drawing a conclusion.

Hint 2

Weight stratum means by their sizes.

Worked solution

State the survey question, population, sampling and measurement rules before drawing a conclusion.
Calculate or simplify this relation.
$\bar x=[20(6)+40(2)]/8=25$
A simple average of the two means would incorrectly ignore the unequal sizes.

The requested value is 25.

Checks and common pitfalls: A simple average of the two means would incorrectly ignore the unequal sizes.

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

Teacher preparation and assessment

Use statistical case study to state a justified conclusion.
Full investigation: Define the target, collect compatible data, analyze and report limitations.
Ethical reporting: Use anonymous classroom data and preserve uncertainty and exclusions.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Define the target, collect compatible data, analyze and report limitations.
Expected reasoning: Use anonymous classroom data and preserve uncertainty and exclusions.
Expected correction: A statistical association alone is not a causal conclusion.