Types of Data and Sampling
Before you can analyse data, you must first collect it, and how you collect it determines everything that follows. A survey that only asks people in a shopping centre will produce very different results from one that randomly samples the whole population. This lesson introduces data classification and sampling methods, showing you how study design shapes conclusions.
Practise this lesson
Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.
A school wants to know how students feel about the canteen menu. They ask the first 50 students who arrive at the canteen at lunch.
Before reading onwill this give a fair representation of all students? What groups might be missed? Write your gut feeling.
Two questions underlie every statistical study: what type of data are you collecting? and how are you selecting who to ask?
Categorical data: data grouped into categories, nominal (no order) or ordinal (ordered).
Numerical data: data that can be counted or measured, discrete (whole counts) or continuous (any measurable value).
Bias: a systematic error that causes a sample to misrepresent the population. A biased sample produces misleading conclusions regardless of how sophisticated the analysis.
Key facts
- Types of data: categorical and numerical
- Common sampling methods
- Sources of bias
Concepts
- Why sampling method matters
- How bias affects results
- When each data type applies
Skills
- Classify data types correctly
- Identify bias in studies
- Design better surveys
Categorical data groups items into categories:
- Nominal: Categories with no natural order, eye colour, gender, blood type, brand preference.
- Ordinal: Categories with a natural order, satisfaction ratings (poor, fair, good, excellent); year level.
Numerical data involves numbers:
- Discrete: Countable values, always whole numbers, number of children, goals scored, test score out of 100.
- Continuous: Measurable values that can take any value in a range, height, weight, time, temperature.
| Variable | Type |
|---|---|
| Shoe size | Discrete numerical |
| Hair colour | Nominal categorical |
| Income level (low / medium / high) | Ordinal categorical |
| Temperature in °C | Continuous numerical |
Categorical data: nominal (no order, eye colour) or ordinal (ranked, survey ratings). Numerical data: discrete (counted, number of goals) or continuous (measured, height). The data type determines which graphs and statistics are appropriate.
Pause, copy the four data types with one example each: nominal categorical (eye colour), ordinal categorical (survey ratings), discrete numerical (goals scored), continuous numerical (height in cm), and note that the type determines which graphs and statistics are appropriate into your book.
Quick check: A student records whether classmates prefer coffee, tea or water. What type of data is this?
We just saw that data is classified as categorical (nominal or ordinal) or numerical (discrete or continuous) before collection, and that the data type determines the appropriate display and analysis. That raises a question: once you know your data type, how do you decide who to ask and ensure the sample represents the population? This card answers it → four sampling methods (simple random, systematic, stratified, convenience) differ in how well each represents all subgroups.
A population is the entire group being studied. A sample is the subset selected for study. Because populations are often too large to survey entirely, we use sampling methods.
Common sampling methods:
- Simple random sampling: Every member has an equal chance of selection. Best for fairness and generalisability.
- Systematic sampling: Select every $n$th person from a list (e.g., every 10th name in a phone book).
- Stratified sampling: Divide the population into subgroups (strata) then randomly sample from each proportionally.
- Convenience sampling: Ask whoever is easiest to reach. Quick but prone to bias.
- Self-selected sampling: People volunteer to respond. Often unrepresentative, strongly-opinionated individuals over-respond.
Sampling methods: simple random (every member equal chance), systematic (every nth member), stratified (proportional from each subgroup), convenience (nearest available, high bias risk). Random methods reduce bias; stratified preserves subgroup proportions.
Pause, copy the four sampling methods and their bias risk: simple random (low bias, every member equal chance), systematic (low bias, every nth member), stratified (low bias, proportional from each subgroup), convenience (high bias, nearest available) into your book.
True or false: Stratified sampling divides the population into subgroups and then randomly samples from each group.
Worked examples · reveal each step
A university surveys students about transport by standing at the bus stop and asking the first 100 people. Identify the data types involved, the sampling method, and two groups likely to be underrepresented.
A company claims "9 out of 10 dentists recommend our toothpaste" based on a survey of 50 dentists at a conference sponsored by the company. Identify three sources of bias.
We just saw that the sampling method affects how representative the sample is, random methods reduce bias while convenience sampling is high-risk. That raises a question: even with a well-chosen method, what specific problems can still make the sample mislead? This card answers it → four bias sources (undercoverage, non-response, leading questions, voluntary response) each distort results in a predictable direction that the researcher may not notice.
Bias occurs when a sample systematically favours certain outcomes over others.
Types of bias:
- Selection bias: The sample does not represent the population (e.g., only asking morning shoppers about shopping habits).
- Measurement bias: Questions are leading or poorly worded (e.g., "Do you agree that our excellent school needs more funding?").
- Non-response bias: Those who respond differ systematically from those who do not, often because satisfied people don't bother replying.
- Confirmation bias: Interpreting data to support pre-existing beliefs and discarding contradictory evidence.
Reducing bias:
- Use random sampling where possible.
- Ensure an adequate sample size.
- Use neutral, clearly worded questions.
- Follow up with non-respondents.
Bias sources: undercoverage (some groups missed), non-response bias (only certain people respond), leading questions, and voluntary response bias. Each distorts results in a predictable direction, identify the direction, not just that bias exists.
Pause, copy the four bias sources and how each distorts results: undercoverage (some groups not reached), non-response bias (only certain people respond), leading questions (wording steers answers), voluntary response bias (self-selected strong opinions dominate) into your book.
Fill the gap: When a sample systematically favours certain outcomes over others, this is called .
Common errors · traps that cost marks
Match each data example to its type:
Quick-fire practice · 2 activities
Classify each variable: number of pets, blood type, exam mark out of 100, postcode, satisfaction rating (1–5 stars), weight in kg. State the type (nominal / ordinal / discrete / continuous) for each.
A survey asks: "Do you agree that our excellent school deserves more funding?" (a) What type of bias is this? (b) Rewrite the question to be neutral. (c) Suggest a sampling method to survey all year groups fairly.
Top 3 list: Describe THREE real-world situations where bias could seriously distort statistical conclusions. For each, name the type of bias and explain how it skews the result.
No, asking the first 50 students at the canteen is not fair. Students who regularly use the canteen are overrepresented, while those who bring lunch or eat elsewhere are missed entirely. There may also be year-group bias if younger students have earlier lunch times. A better approach: a stratified random sample randomly select students from each year group and ask them regardless of where they eat.
What changed in your understanding? What did you predict correctly? What surprised you?
Pick your answer, then rate your confidencethat tells the system what to drill next.
Q1. A researcher records patients' pain levels as: none, mild, moderate, severe. What type of data is this?
Q2. Selecting every 10th student from an alphabetical enrolment list is an example of:
Q3. Which variable is best described as continuous numerical?
Q4. An online poll allows anyone to vote once. The main source of bias is:
Q5. A postcode such as 2000 is best classified as:
SA 1. Classify each variable and justify your answer: (a) number of siblings, (b) favourite subject, (c) height in cm, (d) exam grade (A/B/C/D), (e) time to run 100 m, (f) postcode. (2 marks)
SA 2. A university surveys students about transport by standing at the bus stop and asking the first 100 people. (a) Identify the sampling method. (b) Name two groups likely to be underrepresented. (c) Suggest a better sampling method. (2 marks)
SA 3. A company claims "9 out of 10 dentists recommend our toothpaste" based on a survey of 50 dentists at a conference sponsored by the company. (a) Identify at least three sources of bias. (b) Explain how each could inflate the reported recommendation rate. (c) Design a study that would produce more reliable results. (3 marks)
Comprehensive answers (click to reveal)
MC 1, C: Pain levels (none / mild / moderate / severe) have a natural order but are not numbers, ordinal categorical.
MC 2, B: Every 10th person from a list is the definition of systematic sampling.
MC 3, A: Time is measurable and can take any value in a range, continuous numerical.
MC 4, D: Anyone can vote, so only motivated people do, self-selection bias.
MC 5, B: Postcodes are identifiers with no mathematical meaning, nominal categorical.
SA 1 (2 marks): (a) Discrete numerical. (b) Nominal categorical. (c) Continuous numerical. (d) Ordinal categorical. (e) Continuous numerical. (f) Nominal categorical, postcodes are identifiers, not quantities. [1 mark per 3 correct; 2 marks total].
SA 2 (2 marks): (a) Convenience sampling [0.5]. (b) Students who drive / cycle / walk / use trains; students at different times of day [0.5]. (c) Stratified random sample by faculty and year level, with online and in-person options [1].
SA 3 (3 marks): (a) Selection bias (conference attracts supporters), response bias (social pressure at sponsor event), small sample ($n = 50$) [1]. (b) Dentists feel obligated to respond positively; small $n$ produces high variability; sponsor may have used leading questions [1]. (c) Independent body, random sample of 500+, neutral wording, anonymous responses, stratified by region [1].
Drill 1: Pets: discrete numerical. Blood type: nominal categorical. Exam mark: discrete numerical. Postcode: nominal categorical. Satisfaction rating: ordinal categorical. Weight: continuous numerical.
Drill 2: (a) Measurement bias (leading question). (b) "Do you think the school needs more funding?" (c) Stratified random sample by year group.
Five timed questions on data types, sampling methods and sources of bias. Beat the boss to bank a tier, gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.
⚔ Enter the arenaClimb platforms by answering questions on data and sampling. Pool: lesson 1.
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