GCSE Mathematics 06 — Statistics

Public

Topics include Types of Data & Collection, Sampling Methods, Bias & Survey Design, Basic Charts & Representations, Averages & Spread (Ungrouped Data), Grouped Data & Frequency Polygons, Scatter Graphs & Correlation, and Cumulative Frequency & Box Plots.

Mathematics EN

226 cards

Study this deck on Deckloop

Preview Cards

A sample of cards from this deck.

Example explainer

A sample of the AI explainer you can generate for cards in this deck.

Sampling Methods

Methods for selecting a subset of a population to estimate its characteristics, ensuring fair representation.

Key points

A Census surveys the entire population (accurate but expensive/time-consuming). A Sample surveys a subset.
Simple Random Sampling: Every member has an equal chance of selection (use a random number generator).
Stratified Sampling: Dividing population into groups (strata) and sampling proportionally. Formula: $\frac{\text{Stratum Size}}{\text{Population Size}} \times \text{Sample Size}$ .
Systematic Sampling: Selecting items at regular intervals (e.g., every 10th person) from a list.
Capture-Recapture: Used to estimate population size $N$ for animals. Formula: $\frac{M}{N} = \frac{m}{n}$ (where $M$ =marked initially, $n$ =caught second time, $m$ =marked in second catch).

Worked example

Question

A school has 600 boys and 400 girls. You want a stratified sample of 50 students. How many girls should be selected?

Solution

1. Calculate total population:

600 + 400 = 1000

.
2. Calculate the proportion of girls:

\frac{400}{1000} = 0.4

.
3. Multiply by sample size:

0.4 \times 50 = 20

.

Answer: 20 girls.

Common pitfalls

Using a calculator's random function incorrectly (e.g., getting repeated numbers and not discarding them).
In stratified sampling, rounding the number of people in a way that changes the total sample size.
Forgetting the assumptions of capture-recapture (no migration, tags stay on, random mixing).

Prerequisites

Proportions and ratios
Basic algebra (for capture-recapture)

Further resources

Sampling Strategies
Overview of all main sampling methods with pros and cons.

BBC Bitesize · article