LEARN · EXPLAIN · REVISE

For observations k,k+2,k+4, find variance using denominator 3 as specified.

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

Center the data before squaring; use the stated denominator.

Worked solution

Translate counts into sample proportions and keep classes, units and uncertainty visible.
Calculate or simplify this relation.
$v=[(-2)^2+0^2+2^2]/3=8/3$
This descriptive variance differs from an unbiased sample variance using n−1.

The requested value is 2.66666667.

Checks and common pitfalls: This descriptive variance differs from an unbiased sample variance using n−1.

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.