When we work with data sets we often treat them differently if the data set represents a sample of populations versus the whole population itself.
When we use of the term “population” in common dialogue, we think of groups of people. We may be speaking of people in our town, our state or our country.
The US Census Bureau estimated the population of Colorado, my state, to be 5,540,545 on July 1st 2016. The population of the United states is estimated in 2016 to be 323,127,513. And the population of the world is estimated to be 7.488 billion people.
We can estimate the respective characteristics of a populations such as gender, age, marital status, political affiliation, religion, height, weight, hair color, eye color, etc.
The term population in statistics has a different meaning. "Population” in statistics represents the members of a defined group, a sub-group of the population that we can analyze. WE can collect data on a sample of the world population but it is impossible to collect data on the world's population because that means collecting data on every person on the planet.
So a partial sub-set of the population is called a sample. A sample represents a proportion of a population, a segment or part of a population, and all of the sample's characteristics. A sample is statistically realistic if it is a scientifically-selected sub-group that has the same characteristics as the population. You can acquire a statistically realistic and representative sample by acquiring randomly sampled selections from the population.
Randomly drawn samples must satisfy two requirements:
What is great about random samples is that you can generalize to the population that you are interested in. So if you sample 500 households in your community, you can generalize to the 50,000 households that live there. Think of a sample as a slice of the whole pie. If you match some of the demographic characteristics of the 500 with the 50,000, you will see that they are surprisingly similar. That is the beauty of a sample!
We can obtain data about all the voters in my state and that is a sample of the population of the state, although it might be skewed for most applications because registered voters may have different characteristics than non-registered residents of the state.
Wikipedia says this about a "statistical population" :
"In statistics, a population is a set of similar items or events which is of interest for some question or experiment.[1] A statistical population can be a group of actually existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).[2] A common aim of statistical analysis is to produce information about some chosen population."
And then says this about a "statistical sample":
"In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined procedure.[1] The elements of a sample are known as sample points, sampling units or observations."
NOTE: many vCalc equations are embedded throughout vCalc descriptive pages like this page. Even though they may not stand out in the text, if you hover over the name of an equation it will likely be linked to an actual, pop-up executable equation. For example: Arithmetic Mode