A foundation of a few key terms must be understood before one can progress at all into the study of statistics.

Populations, Parameters, Samples, and Statistics

A population in statistics refers to the entire group of people or objects we’re studying.

I say objects because although in statistics we often study people, studies of inanimate and abstract things are also done.

The key concept behind a population is that the total number of a population is usually unknowable.

If all of a population was known and measurable we could just apply probability to study it, and have not much need for statistics.

In a way, the science of statistics exists because we need a way to study and learn about large groups (aka populations) that would be impossible to measure by studying each individual member of that group.

Think about it. The population of a vast country like the United States is not truly knowable. There is a census done every ten years, and although the numbers from that give us a good idea of the total population, with people being born and dieing every day, there is no way to be 100% accurate.

Consider this in an even more abstract way. Say we’re running a statistical analysis of the free throws done by a professional basketball player.

What’s the population of free throws?

If we’re taking averages of how many free throws the player made out of the total number of free throws they attempted it’s easy to say the population is the total number of free throws attempted.

But this is not correct.

The true population is actually the total number of free throws that player will ever attempt over the course of his or her lifetime, which makes the population at the time of the study unknowable.

Examples of Population:

• The citizens of the United States
• The free throws a basketball player makes over his or her lifetime

It would be impossible to survey each and every individual citizen of the United States and get their preference of political candidate. However, using the science of statistics we create polls that allow us to track and measure the popularity of candidates leading up to election day.

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A sample is simply a subset or part of the population.

A sample is always understood and defined in the context of the population.

If our population is all the citizen’s of the United States then an example of a sample might be 1,000 people chosen at random from the state of Iowa.

Examples of Population and Sample:

Population: Citizen’s Of The United States

Sample: 1,000 random residents from Iowa

To return to the free throw analogy our population would be the total number of free throws ever attempted in that players life, and the sample size would be the number of free throws we recorded as we observed the player.

People easily confuse statistics with parameters and vice versa, so let’s get in to what makes them different.

A parameter is a figure or numeric value that describes an entire population.

An example of a parameter could be something like, “The long run proportion of citizens living in the United States who eat fast food more than twice a week”.

A statistic is a figure or numeric value that describes a sample.

An example of a statistic could be, “Out of 1000 citizens chosen at random from the state of Iowa, 52% ate at fast food over four times a week.”

Without actually surveying every member of a population we can study samples from that population and based on our findings make predictions and generalizations about the entire population.

This practice of studying a sample to make predictions or assumptions about the entire population is known as inferential statistics.

When delineating between whether something is a parameter or statistic ask yourself the following questions?

Is the figure in question describing an entire population or a sample of a population?

If it is about a population then it is a parameter, and if it is talking about a sample or subset of the population then it is a statistic.

An easy mnemonic to remember that parameters describe populations and statistics describe samples of a population is to look at the first letter of each word.

Parameter Population both begin with P

Statistic and Sample both begin with S

I hope after reading this that you feel confident in your understanding of population, parameters, samples, and statistics.

If anything was unclear or you have any feedback, please feel free to reach out to me.

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