LEARN · EXPLAIN · REVISE

A sample’s mean is k and one extreme observation 100k is added. Must the median change as much as the mean? Explain.

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

高一必修第二册(A版).pdf · 9.2 · PDF 200 / printed page 193

TOPIC 01

Estimating a population from a sample

Build understanding of estimating a population from a sample 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#Your turn

k=3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate counts into sample proportions and keep classes, units and uncertainty visible.

Hint 2

Compare value weighting with order statistics.

Worked solution

Translate counts into sample proportions and keep classes, units and uncertainty visible.
Calculate or simplify this relation.
$\bar x_{new}=(n\bar x+100k)/(n+1)$
The change in the median depends on the ordered data; it cannot be inferred from the mean alone.

No. The mean uses numerical magnitudes; the median mainly depends on ranks.

Checks and common pitfalls: The change in the median depends on the ordered data; it cannot be inferred from the mean alone.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment

What must be true before using the main rule for estimating a population from a sample?
Which representation makes this task easier, and why?
Change one assumption. Does the conclusion survive?

Use estimating a population from a sample to state a justified conclusion.
Distribution estimates: Use frequency, class density and sample proportions to describe data.
Location and spread: Mean, median, quantiles and variance answer different questions about the distribution.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Use frequency, class density and sample proportions to describe data.
Expected reasoning: Mean, median, quantiles and variance answer different questions about the distribution.
Expected correction: A sample estimate is not a known exact population parameter.