Difficulty: Beginner | Prerequisites: None
Statistics is the science of collecting, organising, summarising, and analysing data, and then drawing conclusions from it. Every field that works with data (business, government, health, engineering) relies on statistical methods. This first chunk of the course lays the vocabulary and the logic of sampling, both of which underpin everything that follows. If you are coming in cold, start here.
Statistics splits into two branches: descriptive (summarise what you have) and inferential (use a sample to say something about a larger group). Before you can do either, you need to understand what populations, samples, parameters, and statistics are, and how to collect data without introducing bias. Sampling method choice matters because it determines whether your conclusions generalise.
Descriptive statistics
Methods for organising, summarising, and presenting data in an informative way.
In simple terms, this is the "here is what the data looks like" branch. Think averages, tables, charts.
Inferential statistics
Methods used to determine something about a population on the basis of a sample, or for making decisions and drawing conclusions.
Think of it as using a small, carefully chosen group to make educated guesses about the whole group.
Population
A collection, or set, of all units (people, objects, events) that we are interested in studying. May be finite or infinite.
In simple terms, the entire group you care about. If you want to know the average height of all UCF students, the population is every UCF student.
Sample
A subset of the units of a population.
Think of it as the slice of the population you actually measure.
Parameter
A numerical value summarising all the data of an entire population.
In simple terms, the "true answer" for the whole group (often unknown, which is why we sample).
Statistic
A numerical value summarising the sample data.
Think of it as the estimate you compute from your sample. It stands in for the parameter.
Variable
A characteristic about each individual element of a population or sample.
For example, "height" or "favourite colour" – the thing you are measuring or recording for each unit.
Data (singular)
The value of the variable associated with one element of a population or sample. May be a number, word, or symbol.
Data (plural)
The set of values collected for the variable from each of the elements belonging to the sample.
Experiment
A planned activity whose results yield a set of data.
The entire population may be difficult or impossible to reach.
Resources (time, money, personnel) are limited.
Some measurements destroy the item being tested (e.g. crash-testing every car off the line would leave none to sell).
A good sample mirrors the characteristics of the population it represents. If it does not, conclusions drawn from it will be unreliable.
With replacement: a member of the population may be chosen more than once. Each draw is independent of the last.
Without replacement: a member may be chosen only once. Most real-world surveys work this way.
Random sampling means every member of the population has an equal chance of being selected. This is the foundation of valid inference.
Non-random sampling does not guarantee equal selection probability, which introduces the risk of bias.
Simple random sample (SRS): every possible sample of size n has the same chance of being selected. The gold standard, but can be impractical for very large or geographically spread populations.
Stratified random sample: divide the population into non-overlapping subgroups (strata), then take a simple random sample from each stratum. Useful when subgroups differ meaningfully (e.g. sampling by age bracket or region).
Cluster sample: divide the population into non-overlapping groups (clusters), then randomly select entire clusters and include all members of the chosen clusters. Useful when a complete population list is unavailable but clusters are natural (e.g. schools, city blocks).
Systematic sample (1-in-k): pick a random starting point among the first k individuals in an ordered list, then select every kth individual after that. Quick and practical when data is already in a list or queue.
Convenience sampling: selecting individuals or items simply because they are easy to access. Fast and cheap, but highly prone to bias and generally unsuitable for formal inference.
Polling companies use stratified sampling to ensure every demographic is represented before an election. Quality-control teams in manufacturing use sampling (often systematic) because testing every unit is either too expensive or would destroy the product.
Students often confuse a parameter with a statistic. Remember: parameter describes the population (think "p" for population, "p" for parameter); statistic describes the sample.
Students sometimes assume "random" means haphazard. Random sampling is deliberate and structured; every unit's chance of selection is known.
Cluster sampling and stratified sampling look similar on the surface, but they work in opposite directions: stratified sampling takes some members from every subgroup; cluster sampling takes all members from some subgroups.
Convenience sampling is not a type of random sampling, even if the people you happened to grab seem diverse.
⚠️ Be able to identify which sampling method a scenario describes. Exam questions often present a real-world example and ask you to name the method.
⚠️ Know the difference between a parameter and a statistic, and be able to identify each in a word problem.
⚠️ Understand why sampling is necessary (the three reasons above appear regularly in multiple-choice questions).
⚠️ Distinguish between sampling with replacement and sampling without replacement.
True or False: A statistic describes a population.
Fill in the blank: In ______ sampling, the population is divided into strata and a random sample is drawn from each stratum.
True or False: Convenience sampling gives every member of the population an equal chance of being selected.
Fill in the blank: A ______ is a numerical value summarising all the data of an entire population.
True or False: In cluster sampling, you select some clusters at random and then include all members of those clusters.
Answers: 1. False (it describes a sample). 2. Stratified. 3. False. 4. Parameter. 5. True.
Q: A factory tests every 50th lightbulb coming off the assembly line, starting from a randomly chosen bulb among the first 50. What sampling method is this?
A: Systematic sampling (1-in-k, where k = 50).
Q: A researcher divides a city into neighbourhoods, randomly selects five neighbourhoods, and surveys every household in those five. What sampling method is this?
A: Cluster sampling.
Q: What is the key difference between a parameter and a statistic?
A: A parameter summarises data for the entire population; a statistic summarises data for a sample drawn from that population.
Q: Give one reason why we use samples rather than measuring the entire population.
A: Any of: the population may be too large or inaccessible; resources are limited; measurement may be destructive.
Q: In stratified sampling, why do we divide the population into strata before sampling?
A: To ensure each important subgroup is represented in the sample, which reduces sampling error and improves the precision of estimates.
This material connects directly to inferential statistics later in the course, where you will use sample statistics to estimate population parameters and test hypotheses. The quality of your inference depends entirely on how well your sample represents the population, which is why sampling method selection matters here. It also ties into probability (Chapter 3), since random sampling relies on every unit having a known probability of selection.
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