Everything else is ready: study the parts, the key terms and the quiz below.
Samples, Sampling Distributions and the Central Limit Theorem
See how an estimate changes across samples, without requiring a formal central-limit-theorem proof.
In this lesson6 parts
- 01Define the quantity we want to estimate
- 02One sample produces one estimate
- 03Repeat the design to reveal a distribution
- 04Increase the sample size
- 05Why a normal reference needs checking
- 06Reproduce the calculation and state its scope
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- population
- All units in the declared target frame: here, the 19,960 gross positive invoice IDs.
- sampling unit
- One eligible invoice ID, the unit a draw selects.
- population mean
- Average over every unit in the declared frame: £534.40.
- sample
- Selected units from the declared population.
- sample statistic
- A number calculated from the selected sample, such as its mean.
- sampling without replacement
- One ID appears at most once in a draw; the full frame is available again for the next draw.
- sampling distribution
- Distribution of a statistic across repeated samples under one design.
- standard error
- Spread of a statistic across repeated samples.
- empirical standard error (narration)
- The SD of the simulated sample means: £370.99 at 25 IDs.
- finite-population correction
- Reduction in sampling spread when draws use a substantial fraction of a finite frame: √((N − n) / (N − 1)).
- central limit theorem
- Under suitable conditions, standardized sample means approach a normal distribution as sample size increases; it gives no fixed sample size.
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is Stats 5.1 and 5.3 · Sampling distributions and confidence intervals.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.