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.

TOPIC 01

Statistics: mixed assessment

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

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

01 / Transfer#Your turn

k=11

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