Populations and Samples
Population: The entire group of individuals or objects about which information is sought. This is the complete set you want to draw conclusions about.
Sample: A subset of the population selected for study. Because studying an entire population is often impractical, we analyse the sample and use its results to make inferences about the population.
The relationship between population and sample is fundamental to statistics: we collect data from the sample, perform analysis, and then generalise our findings back to the wider population.
A researcher wants to estimate the average height of all 16-year-olds in Spain (the population). Measuring every single student is impossible, so they randomly select 800 students from schools across the country (the sample). The average height of those 800 students is used to estimate the average height of all Spanish 16-year-olds.
The quality of any statistical conclusion depends critically on how well the sample represents the population. A poorly chosen sample can produce misleading results no matter how carefully the mathematics is done.
Types of Data: Discrete and Continuous
Before collecting or analysing data, you must identify what kind of data you are dealing with, since this affects which statistical methods and graphs are appropriate.
Discrete Data: Data that can only take specific, separate (countable) values , usually whole numbers. Gaps exist between possible values.
Continuous Data: Data that can take any value within a given range. It arises from measurement and has no gaps between possible values (limited only by the precision of the measuring instrument).
| Feature | Discrete | Continuous |
|---|---|---|
| How obtained | Counting | Measuring |
| Possible values | Specific, separate | Any value in a range |
| Examples | Number of students, goals scored, pets owned | Height, mass, temperature, time |
A quick test: ask yourself "Can this variable take a value of, say, 3.7?" If the answer is naturally no (e.g. number of siblings), it is discrete. If yes (e.g. height in cm), it is continuous.
Age is often treated as discrete ("I am 17") in everyday speech, but it is actually a continuous variable. In statistics, always consider the underlying nature of the measurement, not just how it is commonly reported.