Track 6 · Sampling and the Central Limit Theorem · Lesson 3 of 8
Sampling distributions
Explain what a sampling distribution is, build one from all possible samples, and describe its centre and spread.
Two analysts each survey a random sample of 40 employees and report average commutes of 35 and 40 minutes. Neither made a mistake: different random samples give different answers. The sampling distribution describes exactly how much such answers vary — the foundation of every margin of error and every test.
A parameter is a fixed number describing the population, such as the population mean or proportion . We usually don't know it. A statistic is a number computed from a sample, such as the sample mean or proportion . A statistic changes from sample to sample: this is sampling variability.
The sampling distribution of a statistic is the distribution of its values over all possible samples of the same size drawn the same way. It is not a distribution of data values; each point in it is a whole sample summarised by one number.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Distinguish parameters (fixed, usually unknown) from statistics (vary from sample to sample)
- Build a sampling distribution by listing or simulating all samples of size n
- Explain why the sample mean is unbiased and less variable than individual values
- Tell apart the population distribution, the sample's distribution and the sampling distribution