Start studying
Module 9 · Sampling and Inference Module contents
Module 9  ·  Card 6 / 16intermediate

Sampling Distribution

A sampling distribution is the distribution of a statistic, such as the mean, over many repeated samples of the same size.

Each sample gives a slightly different mean, and the sampling distribution shows how those means spread.

For example, the mean height from many samples of 100 adults clusters tightly around the population's true mean.

By the central limit theorem, the sampling distribution of the mean is close to normal for large enough samples.

It links one sample to the population, because it shows how far a sample mean tends to stray from the true one.

Learn in depth ↓
Module 09 · Sampling and Inference · 16 concepts
In depth  /  15 lines

Sampling Distribution, in more detail

The sampling distribution is the idea that makes inference possible, though nobody ever sees one directly.

In practice there is only one sample, but the sampling distribution describes what many samples would have shown.

It answers how far a single sample's statistic is likely to be from the population value.

Imagine drawing a sample of 100 orders, working out its mean, and repeating that thousands of times.

The thousands of means would form their own distribution, centred on the population mean.

That distribution is much narrower than the distribution of single orders, because averaging cancels out extremes.

The bigger each sample, the narrower the sampling distribution becomes.

By the central limit theorem its shape is close to normal for samples of reasonable size, even when the data is skewed.

Every statistic has a sampling distribution, including medians, proportions and differences between groups.

For heavily skewed data and small samples, the distribution of the mean can still be lopsided.

Simulation can build a sampling distribution directly when no formula exists.

Resampling the one sample many times with replacement, called the bootstrap, is a common way to do that.

Its spread is what every margin of error and every significance test is built on.

In practice, a quick simulation is a good check on whether a formula's answer is sensible.

The usual confusion is between the distribution of the data and the distribution of a statistic, which are very different.

Want the full technical article? Wikipedia ↗
Test yourself

One question on this card. Every option explains itself once you pick, right or wrong.

Question 1
An analyst draws 1,000 random samples of 50 orders each and plots the 1,000 sample means. What does that plot show?
Sampling and Inference

16 concepts in this module, then a graded test with every answer explained.

Study this module →
↑↓ move↵ openesc close