Types of Data & Sampling — GCSE Maths Tutorial, Worked Examples & Practice

Revise Types of Data & Sampling (discrete vs continuous, qualitative vs quantitative, primary vs secondary data and sampling bias) within Statistics — Sampling, aligned to Edexcel, AQA & OCR GCSE (9–1) and International GCSE Maths. The interactive practice tool at the top of this page includes 30 self-marking practice questions across 3 structured skill steps, with instant diagnostic feedback and full worked solutions.

Step 1 of 310 interactive practice questions

Qualitative, Discrete & Continuous Data

Classifying categorical, counted discrete and measured continuous variables

Key Method & Revision Notes

In Statistics, we classify data by whether it describes words/categories or numbers — and whether numbers are counted or measured:
Qualitative: Non-numerical words or labels (e.g. eye colour, favourite sport, car make).
Discrete (Quantitative): Numerical data that is counted or restricted to fixed steps (e.g. number of siblings, goals scored, UK shoe size $5, 5.5, 6$).
Continuous (Quantitative): Numerical data that is measured on a continuous scale and can take any decimal value (e.g. height, mass, time, temperature, foot length in cm).

Worked Example

Question:

Classify each type of data as Qualitative, Discrete, or Continuous:

(a) Number of cars in a car park

(b) Mass of a parcel in kg

Step-by-Step Solution:

(a) Discrete — cars are counted in whole numbers.

(b) Continuous — mass is measured on a continuous scale.

(a) Discrete • (b) Continuous • (c) Qualitative

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 2 of 310 interactive practice questions

Primary vs Secondary Data & Questionnaires

Distinguishing data sources and spotting overlapping or incomplete survey boxes

Key Method & Revision Notes

Data is also grouped by who collected it:
Primary Data
Collected yourself first-hand (your own survey, tally, or science experiment).
Advantage: Reliable & tailored to your exact question.
Disadvantage: Slow & expensive.
Secondary Data
Collected by someone else (Met Office weather tables, ONS census, websites).
Advantage: Quick, cheap & large datasets.

Worked Example

Question:

Criticise this questionnaire item:

"How much exercise do you do?" [ 1–2 hrs ] [ 2–4 hrs ] [ 5+ hrs ]

Step-by-Step Solution:

1. No time frame in the question (per day or per week?).

2. Overlapping boxes ($2$ hours is in both 1–2 and 2–4).

3. Missing values ($0$ hours and $4.5$ hours have no box).

No time frame • Overlapping 2 • Missing 0

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Step 3 of 310 interactive practice questions

Populations, Random Sampling & Bias

Simple random and systematic sampling, population estimates and avoiding bias

Key Method & Revision Notes

A population is the whole group being studied. A sample is a smaller group chosen to represent the population (faster and cheaper than a full census).
Simple Random Sample: Every member of the population has an equal chance of being chosen (e.g. numbering everyone $1$ to $N$ and using a random number generator).
Systematic Sample: Pick a random starting point, then select every $k\text{th}$ item, where $$k = \frac{\text{Population Size}}{\text{Sample Size}}$$
Sampling Bias: Occurs when some members are more likely to be picked than others (e.g. surveying outside a gym at 9 am on Tuesday, or picking a sample that is too small).

Worked Example

Question:

A college has $1500$ students. A systematic sample of $50$ students is taken from the register. Find the sampling interval $k$.

Step-by-Step Solution:

Divide the population size by the required sample size:

$$k = \frac{1500}{50} = 30$$Pick a random student from the first $30$, then select every $30\text{th}$ student.

$$ k = 30 $$

Ready to test this skill? Use the interactive tool at the top of the page to practise 10 self-marking exam-style questions (30 questions loaded in this topic module).

Types of Data & Sampling — GCSE Maths Tutorial, Worked Examples & Practice

Qualitative, Discrete & Continuous Data

Key Method & Revision Notes

Worked Example

Primary vs Secondary Data & Questionnaires

Key Method & Revision Notes

Worked Example

Populations, Random Sampling & Bias

Key Method & Revision Notes

Worked Example

Related GCSE Maths Topics (Sampling)