# Definition: Population

Definition 1 (Healey, 1993, Glossary – p. 548):

The total collection of all cases in which the researcher is interested.

Definition 2 :

In statistics, this is a conventional term for any set of entities or source from which samples are taken.  This may be an actual population of objects, beings or measures, or may simply refer to a probability distribution.

Definition 3:

In sampling theory and more generally, a collection of items about which information is sought.  A sample is taken and inferences are made about the characteristics of the population on the basis of sample evidence.  For example, if, in a random sample of 300 adult Londoners, 90 (i.e. 30 percent) are smokers, then 30 percent is the approximate estimate of the proportion of adult Londoners who smoke.  Confidence limits may be attached to this estimate for a random sample, but not to samples such as quota samples.

Statistical inferences are made about populations, sometimes hypothetical, for which it is believed the observations available could reasonably be regarded as a random sample.  For example, measurements may be made of the thickness of ten sheets of metal randomly selected from the daily production of a factory; while the actual population sampled is only that day’s production, inferences are often taken to apply to a hypothetically infinite population of all such sheets the factory has ever produced or will ever produce under similar conditions.  This concept is based on the assumption that production standards do not change measurably from day to day.

Loosely, the term is sometimes used in phrases such as ‘a sample from a normal population’ to imply that we are assuming that the values of the characteristic we are observing have, in the population we are sampling, a normal distribution.

Definition 4:

The complete set of objects being studied.  A sample is any subset of the population.  For example, we might wish to study the height of 18-year-old men in the UK.  It would be impractical to measure every member of this population (all 18-year-old men in the UK) and so a sample would be taken.

Definition 5:

A population is the complete set of objects (values or people) which is being studied by some statistical method.

Definition 6:

A specified set of objects or outcomes to be measured or observed.

Etymology:

From Latin populous, “people,” of Etruscan origin.  Simply speaking, a population is just a collection of people.  In fact English people is borrowed from French peuple, which developed from Latin populous.  In statistics a population is a set of items, not necessarily people, defined by one or more common characteristics.

## Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.