---
title: "Samples: cheat sheet"
subtitle: "Data and chance"
---

# Samples

> The words and methods from this unit, with an example of each.

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**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_

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**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_

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**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.

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

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**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_

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**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_

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**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.

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

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