Picture of a population and a sample. The little dots are the members.

A population is the set consisting of all the members of the group that we are interested in.

Example 1. Suppose we want to know the average weight of the squirrels in New York City’s Central Park. The population for this would be “all the squirrels in Central Park”. An individual squirrel in Central Park is a member of the Central Park squirrel population.  On the other hand, squirrels living someplace else, like in California or Canada, wouldn’t be considered part of the Central Park squirrel population.

Example 2. If we are studying C02 emissions of automobiles driven in New York, then the population for this situation would be the “all the automobiles driven in New York”.

A sample is a subset of the population.

Example 3. Suppose we are trying to understand CUNY students’ attitudes toward online learning. We survey (ask) 30 CUNY students if they like online learning. The population is all CUNY students and the 30 students in the survey is the sample.

Example 4. Suppose we want to know which are heavier, on average, lions or tigers. In this situation we have two populations: lions and tigers.  To answer that question we would need a sample from the lion population and a sample from the tiger population.
Example 5. If we want to know the average weight of humans the population would be “all humans”.  If we want to know the average weight of adults the population would be all the human adults.

The current (2020) human population is about 7.8 billion people.

When we want to understand a population we take a sample. We gather information from the members of the sample. Then, we make inferences about the population based on what we learned from studying the sample.

Why do we use samples?

Two reasons.

(1) Populations tend to be large. So, it might be prohibitively expensive, too time consuming, or simply physically impossible to gather information from every member of a population.

(2) The sampling process can be destructive.

Example 6. The blood in a blood sample is usually destroyed by the measurements made on it.