A population is the complete group being investigated, while a sample is a smaller group selected from it. Valid conclusions require the sample to represent the population accurately.
Population and Sample Compared
| Concept | Meaning | Example |
|---|---|---|
| Population | Every individual or item relevant to the investigation | All 1,200 students at a school |
| Sample | A subset of the population from which data is collected | 80 students selected from the school |
| Census | Data collection from every member of the population | Surveying all 1,200 students |
Suppose a school wants to estimate students' average weekly study time. The population is all 1,200 students. Because a census may be expensive and time-consuming, the school surveys 80 students.
A numerical measure describing a population is a parameter; the corresponding sample measure is a statistic. The true mean study time of all 1,200 students is a parameter, while the mean for the 80 sampled students is a statistic used to estimate it.
The estimate's reliability depends on sample selection. A random sample gives each eligible member a fair chance of selection, reducing selection bias. A representative sample reflects relevant population characteristics, such as year group or course level.
A common misconception is that a large sample is automatically representative. Size can reduce sampling variation, but a large biased sample may still produce misleading conclusions. Surveying only students in the library, for example, would probably overestimate average study time.
IB Exam Technique
This is SL 4.1: Introduction to Statistics, studied at both SL and HL. In Paper 1 or Paper 2 contexts, identify the population and sample precisely. Then comment on the sampling method, possible bias, and whether generalizing from the sample to the population is justified. Avoid vague statements such as “the population is everyone”; specify everyone relevant to the investigation.
