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Understanding data types and sampling methods is the foundation of all statistics work in GCSE Mathematics. Before you can analyse data, you need to know what kind of data you are dealing with and how to collect it reliably.
| Type | Definition | Examples |
|---|---|---|
| Qualitative (categorical) | Non-numerical; describes qualities or categories | Favourite colour, type of car, eye colour |
| Quantitative | Numerical; can be measured or counted | Height, number of siblings, temperature |
Quantitative data is further divided:
| Type | Definition | Examples |
|---|---|---|
| Discrete | Can only take specific values (often whole numbers); you count it | Number of pets (0, 1, 2, 3, …), shoe size (5, 5.5, 6, …), dice score |
| Continuous | Can take any value within a range; you measure it | Height (172.4 cm), time (13.562 s), mass (68.3 kg) |
Key tip: Ask yourself "Can the value be 3.7 and anything in between?" If yes, it is continuous.
| Type | Definition | Advantages | Disadvantages |
|---|---|---|---|
| Primary | Data you collect yourself (surveys, experiments, observations) | Tailored to your purpose; you control accuracy | Time-consuming and expensive |
| Secondary | Data collected by someone else (internet, newspapers, databases) | Quick to obtain; large samples available | May not be exactly what you need; may be out of date or biased |
Every member of the population has an equal chance of being selected.
How to do it:
Example: A school has 1,200 students. The head teacher wants a sample of 60. She assigns each student a number from 0001 to 1200 and uses a random number generator to pick 60 numbers.
| Advantages | Disadvantages |
|---|---|
| Free from bias | Need a complete list of the population (sampling frame) |
| Easy to understand | May not be representative if sample is small |
Select every kth member from a list after a random start.
How to do it:
Example: Population = 500, sample size = 25. k = 500 ÷ 25 = 20. Start at a random number between 1 and 20, say 7. Select the 7th, 27th, 47th, 67th, … member.
| Advantages | Disadvantages |
|---|---|
| Simple and quick | Need a list; if there is a pattern in the list, results may be biased |
The population is divided into strata (groups) based on a characteristic (e.g. year group, gender). A proportional sample is taken from each stratum.
Formula:
Number from stratum = (number in stratum ÷ total population) × sample size
Worked Example:
A school surveys 50 students. The year groups are:
| Year group | Number of students |
|---|---|
| Year 7 | 180 |
| Year 8 | 200 |
| Year 9 | 190 |
| Year 10 | 160 |
| Year 11 | 170 |
| Total | 900 |
Number from Year 7 = (180 ÷ 900) × 50 = 10 Number from Year 8 = (200 ÷ 900) × 50 = 11.1… ≈ 11 Number from Year 9 = (190 ÷ 900) × 50 = 10.6… ≈ 11 Number from Year 10 = (160 ÷ 900) × 50 = 8.9… ≈ 9 Number from Year 11 = (170 ÷ 900) × 50 = 9.4… ≈ 9
Check: 10 + 11 + 11 + 9 + 9 = 50 ✓
Within each stratum, students are selected using a random method.
| Advantages | Disadvantages |
|---|---|
| Guarantees proportional representation | Need to know the strata sizes |
| More representative than simple random | More complex to organise |
Bias means the sample is not representative of the population — certain groups are over- or under-represented.
| Source | Example |
|---|---|
| Non-random selection | Only surveying your friends |
| Time of collection | Surveying a high street at 10 a.m. on Monday misses workers |
| Leading questions | "Don't you agree that …?" pushes people towards an answer |
| Non-response | People who don't reply may have different views |
| Too small a sample | Fewer people = less likely to be representative |
| Location bias | Only surveying at one location |
Edexcel exam tip: A common question asks you to criticise a sampling method. Look for: too small, not random, only one location, leading questions, or a specific time that excludes groups.
Question: Priya wants to find out how much time students at her school spend on homework. She decides to ask all 30 students in her maths class. Give two reasons why this may not give a representative sample.
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