Population

Population

The entire set of cases or individuals under consideration in a statistical analysis. For example, a poll given to a sample of voters is designed to measure the preferences of the population of all voters.

Example

Problem: A school principal wants to know the average test score of all 800 students enrolled at the school. She randomly selects 50 students and records their scores. Identify the population and the sample.

Step 1: Identify what group the principal wants to learn about. She wants to know the average score of all 800 students enrolled at the school.

Step 2: The population is the entire group of interest: all 800 students at the school.

Step 3: The sample is the subset actually measured: the 50 students whose scores were recorded.

Answer: The population is all 800 students at the school. The sample is the 50 students selected.

Why It Matters

Clearly defining the population is the first step of any statistical study because it determines what conclusions you can draw. If your sample does not represent the population well, your results may be biased and misleading. Population parameters (like the true mean or proportion) are what statisticians ultimately want to estimate, even though they usually can only measure a sample.

Common Mistakes

Mistake: Confusing the population with the sample.

Correction: The population is the entire group you want to study; the sample is the smaller subset you actually collect data from. A statistic describes a sample, while a parameter describes a population.

Related Terms

Sample — A subset drawn from the population
Parameter — A numerical value describing the population
Statistic — A numerical value describing a sample
Census — Collecting data from every population member
Sampling Distribution — Distribution of a statistic over repeated samples