Statistics
Grade 2-4Collecting Data & Sampling Methods
Before any data can be displayed or analysed, it has to be collected in a way that is fair and representative, which is why examiners test whether you can identify types of data, name and apply sampling methods, and spot bias in how a sample was chosen. This lesson covers types of data, the four main sampling methods, calculating a stratified sample, and identifying bias in surveys and questions.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Types of data
Data is qualitative if it describes a quality, such as colour or opinion, and quantitative if it is numerical. Quantitative data is discrete if it can only take exact, separate values, such as a number of goals, and continuous if it can take any value in a range, such as a height or time.
The number of pets owned by each student is quantitative and discrete, since it can only be a whole number. The height of each plant in a garden is quantitative and continuous, since it could be any value, including decimals.
Sampling methods
Random sampling gives every member of the population an equal chance of being chosen, often using a random number generator. Systematic sampling selects members at a fixed interval from an ordered list, such as every 10th name. Stratified sampling divides the population into groups and samples from each group in proportion to its size. Convenience (or opportunity) sampling simply selects whoever is easiest to reach, such as the first people who happen to walk past.
Selecting every 10th name from an alphabetical list of employees is systematic sampling. Asking the first 50 people who walk past a supermarket is convenience sampling.
Calculating a stratified sample
Find the total population, then multiply the sample size by the fraction that each group makes up of the total, to find how many should be sampled from that group.
A school has 180 Year 10 students and 220 Year 11 students, a total of 400. For a stratified sample of 40 students, the number of Year 10 students sampled is 40 × 180/400 = 18.
Identifying bias
A sample is biased if it is not representative of the whole population, often because it excludes certain groups or only includes people who chose to respond. A survey question can also be criticised if it is leading, uses vague or undefined terms, gives overlapping response options, or does not specify a time frame.
Surveying people leaving a football stadium about the most popular sport in a town is biased, since the sample only includes football fans and is not representative of the whole town. Asking "Don't you agree the new park is a great addition?" is a leading question, since it suggests the answer the researcher wants.
Worked Examples
Three exam-style questions, fully solved.
State whether the following data is qualitative or quantitative: the number of pets owned by each student in a class.
Easy- 1.Decide whether the data describes a quality or a number: the number of pets is a numerical value
Answer: Quantitative
A school has 180 Year 10 students and 220 Year 11 students. A stratified sample of 40 students is taken. How many Year 10 students should be sampled?
Medium- 1.Find the total number of students: 180 + 220 = 400
- 2.Multiply the sample size by the fraction of the total that is Year 10: 40 × 180/400
Answer: 18 students
A company wants to know if people prefer their new product. They only survey customers who complete a card sent with the product. Explain why this sample may be biased.
Hard- 1.Identify who is included: only customers who chose to fill in and return the card
- 2.Consider who this excludes: customers who did not respond are left out entirely
Answer: This is self-selection bias, since only people who chose to respond are included, which may not represent the opinions of all customers
Avoid These
The most common mistakes students make.
Confusing discrete and continuous data, for example treating a measurement like height or time as discrete instead of continuous.
Mixing up systematic sampling (fixed intervals from a list) with stratified sampling (proportional groups), since both involve some structure rather than pure randomness.
In a stratified sample calculation, multiplying by the wrong fraction, such as using the sample size divided by one group instead of the group divided by the total population.
Giving a vague reason for bias, such as "it is not fair", instead of explaining specifically who is excluded and why this makes the sample unrepresentative.
When criticising a survey question, only stating that it is "a bad question" instead of identifying the specific issue, such as leading language, vague terms, overlapping options, or no time frame.
FAQ
Questions parents and students ask.
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