Inferential Statistics • Lesson 4

Sampling Distributions

Learn how a statistic such as a sample mean behaves when we take many different samples from the same population.

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Concept 1DEFINITION

What Is a Sampling Distribution?

A sampling distribution is the distribution of a statistic — like the sample mean — across many samples of the same size drawn from the same population. It describes how that statistic behaves, not how the raw data behaves.

Learn by Seeing

Distribution of a statistic

Repeated samples of size n
        ↓
Sample 1 → mean 48
Sample 2 → mean 52
Sample 3 → mean 50
        ↓
Sampling distribution of the sample mean

The distribution of the statistic across repeated samples is the sampling distribution.

From one sample to a sampling distribution

Sample 1

48

sample mean

Sample 2

52

sample mean

Sample 3

50

sample mean

↓

Sampling distribution

48, 52, 50, ... (one value per sample)

Interactive Activity

What is a sampling distribution?

Hint: It is about the statistic, not the raw observations.

Statistics Analyst Mindset

Every estimate has a distribution

Analysts do not just compute one number and stop. They ask how that number would vary across repeated samples. That variation — the sampling distribution — is what makes confidence intervals and hypothesis tests possible.

01

Sample

Draw observations.

02

Statistic

Compute per sample.

03

Repeat

Same size, many times.

04

Distribute

Study the statistics.

Lesson Summary

What you learned

Sampling distribution

The distribution of a statistic across repeated samples.

Sample vs sampling

Raw observations vs statistics across samples.

Center

The mean of the sample means centers on μ.

Variability

Natural spread — smaller for larger n.

Workflow

Population → sample → statistic → repeat.

Why it matters

Foundation for standard error, CIs and hypothesis tests.