Data Collection and Sampling Methods
Section: Statistics | Syllabus: Cambridge Lower Secondary Checkpoint Mathematics (0862)
Types of Data
| Data Type | Description | Example |
|---|---|---|
| Qualitative | Non-numerical, describes qualities | Favourite colour, hair colour |
| Quantitative | Numerical | Height, test score |
| Categorical | Fits into groups or categories | Type of pet, blood group |
| Discrete | Countable, specific values only | Number of siblings, shoe size |
| Continuous | Any value within a range | Height, time, mass |
Data Collection Methods
- Primary data: collected firsthand by the researcher, e.g. a survey you conduct yourself.
- Secondary data: collected by someone else and reused, e.g. government census data.
- Common methods: questionnaires and surveys, observation, experiments, interviews.
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Question: A student wants to find out how much time classmates spend on homework each week. Suggest a suitable collection method and data type.
- Method: a questionnaire asking each student to report their weekly homework hours
- Answer: Data type: quantitative, continuous (time can take any value)
Sampling Methods
A population is the entire group being studied. A sample is a smaller part of the population, used to represent the whole when studying everyone isn't practical.
Stratified sampling: each group is sampled in proportion to its size in the population
- Random sampling: every member of the population has an equal chance of being chosen.
- Systematic sampling: choosing every nth member from a list.
- Stratified sampling: dividing the population into groups (strata) by a characteristic, then sampling proportionally from each group.
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Question: A school has 600 students: 350 girls and 250 boys. Find a stratified sample of 60 students.
- Step 1: Girls: 60 × (350/600) = 35
- Step 2: Boys: 60 × (250/600) = 25
- Check: 35 + 25 = 60 ✓
- Answer: 35 girls, 25 boys
Piloting and Refining a Data Collection Method
Before collecting data on a large scale, it's good practice to trial (pilot) the method on a small scale first - this often reveals practical problems that aren't obvious when just planning on paper, letting you refine the method before committing time to the full investigation.
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Question: A student plans to test the prediction "people with longer arms also have longer legs" by measuring 100 classmates' arm and leg lengths with a tape measure. Suggest why running a small trial of 5 people first would be useful, and how the method might need to change.
- A trial might reveal that classmates feel uncomfortable being measured, or that "arm length" and "leg length" aren't clearly defined (measured from where to where?).
- Answer: Running a trial of 5 people first lets the student spot and fix these issues - e.g. by clearly defining the measurement points - before spending time measuring all 100 classmates with a flawed method.
Choosing an Appropriate Method
Justify a method by referring to the specific statistical question, considering practicality, cost, time, and how fairly it represents the population.
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Question: A company wants to know the average commute time of all 5000 employees nationwide. Explain why a stratified sample by office location might be appropriate.
- Surveying all 5000 employees would take too much time and cost, so a sample is more practical.
- Stratified sampling by office location ensures each office is fairly represented, since commute times may differ significantly between city and rural offices.
Real-World Applications
Data collection and sampling decisions matter across many fields:
- Market research: surveying customer preferences.
- Government census: collecting nationwide population data.
- Scientific studies: sampling participants for medical trials.
- Opinion polls: sampling voters before an election.
- Quality control: sampling products from a factory production line.
Exam Tips
Common Mistakes
MistakeConfusing discrete and continuous data, e.g. calling "number of pets" continuous
Fixdiscrete data is countable in fixed steps; continuous data can take any value in a range
MistakeConfusing qualitative and quantitative data
Fixqualitative data describes qualities (non-numerical); quantitative data is numerical
MistakeSampling only from one group, ignoring the need to represent the whole population
Fixchoose a method like stratified sampling that fairly represents every part of the population
MistakeAssuming a bigger sample size always means the sampling METHOD is unbiased
Fixsample size and sampling method are separate issues - a large sample can still be biased if the method is flawed
MistakeMiscalculating a stratified sample by using the wrong proportion
Fixalways use (group size ÷ total population) × sample size for each stratum
MistakeGoing straight to a full-scale investigation without trialling the method first
Fixa small trial often reveals practical problems (unclear definitions, impractical measurements) that are easy to fix before scaling up
For Exams
- Learn the distinctions: qualitative/quantitative, and categorical/discrete/continuous.
- Justify your choice of method by referring to the specific statistical question.
- For stratified sampling: calculate each group's proportion of the total population first.
- Consider practicality (cost, time) when choosing between a population survey and a sample.
- Run a small trial first, then refine your method based on what you learn.
- Explain WHY a method is appropriate, not just what the method is.
Interactive revision notes, videos and practice questions load below.