Samples: cheat sheet

Data and chance · The words and methods from the lessons, with an example of each.

census and sample

A census is exact but slow and costly; a sample estimates. An experiment changes something on purpose; an observation watches.

\text{census: everyone} \quad \text{sample: some}

A random sample of 20 from a school of 200

sampling methods

Simple random: same chance for all. Systematic: every kth from a random start. Stratified: at random within each group, in proportion. Convenience and quota: someone chooses, so they can be biased.

k = \dfrac{\text{population}}{\text{sample size}}

sampling variation

Fair samples from one population give different results by chance. Their results scatter around the population's value, closer for bigger samples.

\text{bigger samples vary less}

20 samples of 20: results scattered around the school's value

bias

Bias pushes a result one way: sampling bias (who is asked), response bias (how they are asked), measurement bias (the tool). A bigger sample doesn't fix it.

\text{who? how asked? how measured?}

A convenience sample: all from Year 7, pushed high

describing a sample

Describe the shape (symmetric or skewed), the centre (mean, median) and the spread (range), then estimate the population with the method and size. Primary data you collect; secondary data others collected.

\text{shape, centre, spread} \to \text{about } \ldots

A random sample of 40 students' sleep as a dot plot

inference

Infer only about the population sampled, give an estimate, and say how sure you are (size and method). Collect data with consent and anonymity.

\text{about } \ldots \text{, from a random sample of } n