Data Collection and SamplingEdexcel GCSE Maths: Revision notes
Section 1
Sampling and Populations
A population is the entire group being studied; a sample is a smaller group selected from the population to represent it. Because studying an entire population is often impractical, statisticians infer properties of the population from a well-chosen sample.
Larger, more representative samples give more reliable estimates, but sampling always has limitations: a poorly chosen or too-small sample can give a misleading picture of the whole population (this is called bias).
A larger sample is not automatically unbiased — a large but unrepresentative sample (e.g. only surveying one age group) can still give misleading results.
Section 2
Tables and Charts for Categorical Data
Categorical (non-numerical) and discrete ungrouped data can be displayed and interpreted using:
- Frequency tables: list each category with how often it occurs
- Bar charts: bars of equal width, height shows frequency, gaps between bars
- Pie charts: each category is a sector, with angle = (frequency ÷ total) × 360°
- Pictograms: symbols represent a fixed quantity, with a key explaining the scale
If 45 out of 180 people chose 'blue', the pie chart angle for blue = (45 ÷ 180) × 360 = 90°.
Section 3
Time Series Graphs
A time series shows how a quantity changes over time, with time always on the horizontal axis. Points are usually joined with straight lines to show the pattern of change.
Time series graphs are used to identify and describe trends — a general upward, downward, or seasonal (repeating) pattern over time — rather than to read off single exact values.
Section 4
Stem-and-Leaf Diagrams
A stem-and-leaf diagram displays numerical data by splitting each value into a 'stem' (e.g. the tens digit) and a 'leaf' (e.g. the units digit), keeping every original data value visible while showing the overall shape of the distribution.
A back-to-back stem-and-leaf diagram places two data sets on either side of a shared stem, making direct comparison of two data sets straightforward. Leaves must always be written in ascending order, and a key must be given to explain how to read the values.
Always check for and include a key (e.g. '3 | 4 means 34') — without it, the diagram cannot be read correctly.
Section 5
Choosing the Right Diagram
Different data types need different representations:
| Data type | Suitable diagram |
|---|---|
| Categorical | Bar chart, pie chart, pictogram |
| Discrete, small range | Stem-and-leaf, frequency table |
| Continuous or over time | Time series graph, histogram |
| Comparing two data sets | Back-to-back stem-and-leaf, dual bar chart |
Choosing an inappropriate diagram for the data type can make the data harder to interpret or misleading.
Must Know
- A sample is used to infer properties of a population; larger and more representative samples give more reliable estimates
- Sampling has limitations — bias occurs when a sample does not fairly represent the population
- Pie chart sector angle = (frequency ÷ total frequency) × 360°
- Time series graphs have time on the horizontal axis and are used to identify trends
- Stem-and-leaf diagrams keep every data value visible; back-to-back versions compare two data sets
- Choose the diagram type to match the data (categorical, discrete, continuous, or comparative)
That's the notes covered.
Carry on to the next subtopic.