## What is the population?

In statistics, a population is the entire pool from which a statistical sample is drawn. A population can refer to an entire group of people, objects, events, hospital visits or measures. A population can therefore be considered as an aggregated observation of subjects grouped by a common trait.

Unlike a sample, when statistically analyzing a population, there are no standard errors to report, that is, these errors inform analysts who use a sample of the measure in which their estimate may deviate from the real value of the population. But since you work with the real people, you already know the real value.

The United Nations has designated July 11 as World Population Day.

## The bases of the population

A population can be defined by any number of characteristics within a group that statisticians use to draw conclusions about the subjects of a study. A population can be vague or specific. Examples of population (loosely defined) include the number of newborns in North America, the total number of tech startups in Asia, the average size of all CFA exam candidates worldwide, the average weight of taxpayers Americans, etc.

Population can also be defined more specifically, such as the number of newborn babies in North America with brown eyes, the number of startups in Asia that have failed in less than three years, the average size of all candidates for the exam. CFA, the average weight of all American taxpayers over 30, among others.

Most of the time, statisticians and researchers want to know the characteristics of each entity in a population, in order to draw the most precise conclusion possible. However, this is impossible or impractical most of the time, as the population sets tend to be quite large.

For example, if a business wanted to know if each of its 50,000 customers served during the year was satisfied, it could be difficult, costly, and inconvenient to call each customer by telephone to conduct a survey. Since the characteristics of each individual in a population cannot be measured due to constraints of time, resources and accessibility, a sample of the population is taken.

10 billion

The amount by which the world’s population is expected to increase by the middle of the 21st century.

### Population samples

A sample is a random selection of members of a population. It is a smaller group drawn from the population that presents the characteristics of the entire population. The observations and conclusions drawn from the sample data are attributed to the population.

The information obtained from the statistical sample allows statisticians to develop hypotheses on the larger population. In statistical equations, the population is generally indicated by a capital letter *NOT* while the sample is usually indicated by a lowercase *not.*

### Population parameters

A parameter is a data based on an entire population. Statistics such as means and standard deviations, when taken from populations, are called population parameters. The population mean and the population standard deviation are represented by the Greek letters µ and σ, respectively.

The standard deviation is the variation in the population deducted from the variation in the sample. When the standard deviation is divided by the square root of the number of observations in the sample, the result is called the standard error of the mean.

While a parameter is a characteristic of a population, a statistic is a characteristic of a sample. Inferential statistics allow you to make an educated guess about a population parameter based on a statistic calculated from a random sample from that population.

Key points to remember

- In statistics, a population is the entire pool from which a statistical sample is drawn.
- Examples of populations may be the number of newborns in North America, the total number of tech startups in Asia, the average size of all CFA exam candidates worldwide, the average weight of American taxpayers, etc. .
- The populations can be contrasted with the samples.

## Real example of population

For example, suppose a denim clothing manufacturer wants to check the quality of the seams on their jeans before shipping them to retail stores. It is not profitable to examine every pair of jeans that the manufacturer produces (the population). Instead, the manufacturer examines only 50 pairs (one sample) to draw a conclusion as to the probability that the entire population has been correctly sewn.