Statistical population

# Statistical population

Overview
A statistical population is a set of entities concerning which statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...

s are to be drawn, often based on a random sample
Random sample
In statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...

taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest. Notice that if we choose a population like all crows, we will be limited to observing crows that exist now or will exist in the future. Probably, geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

will also constitute a limitation in that our resources for studying crows are also limited.
Discussion
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Encyclopedia
A statistical population is a set of entities concerning which statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...

s are to be drawn, often based on a random sample
Random sample
In statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...

taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest. Notice that if we choose a population like all crows, we will be limited to observing crows that exist now or will exist in the future. Probably, geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

will also constitute a limitation in that our resources for studying crows are also limited.

Population is also used to refer to a set of potential measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

s or values, including not only cases actually observed but those that are potentially observable
Observable
In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...

. Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire
Cambridgeshire
Cambridgeshire is a county in England, bordering Lincolnshire to the north, Norfolk to the northeast, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west...

, and we want to know the mean weight of these birds. For each bird in the population of crows there is a weight, and the set of these weights is called the population of weights.

## Subpopulation

A subset
Subset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...

of a population is called a subpopulation. If different subpopulations have different properties, the properties and response of the overall population can often be better understood if it is first separated into distinct subpopulations.

For instance, a particular medicine may have different effects on different subpopulations, and these effects may be obscured or dismissed if such special subpopulations are not identified and examined in isolation.

Similarly, one can often estimate parameters more accurately if one separates out subpopulations: distribution of heights among people is better modeled by considering men and women as separate subpopulations, for instance.

Populations consisting of subpopulations can be modeled by mixture model
Mixture model
In statistics, a mixture model is a probabilistic model for representing the presence of sub-populations within an overall population, without requiring that an observed data-set should identify the sub-population to which an individual observation belongs...

s, which combine the distributions within subpopulations into an overall population distribution.

• Population
Population
A population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that inter-breeding is possible between any pair within the area and more probable than cross-breeding with individuals...

• Sample (statistics)
Sample (statistics)
In statistics, a sample is a subset of a population. Typically, the population is very large, making a census or a complete enumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size...

• Sampling (statistics)
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....