# Statistical Variable

### From MM*Stat International

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An observable characteristic of a statistical element is called variable.
The actual values assumed by statistical variables are called observations, measurements or data.
The set of possible values a variable can take is called sample space.
Variables are denoted by script capitals , whereas corresponding realizations are written in lower case: , the indices reflect the statistical elements sampled.

Variable | Observations |
---|---|

It is useful to differentiate between variables used for identification and target variables.
*Identification variables*
In assigning a set of fixed values the elements of the population are specified. For example, restricting a statistical investigation to female persons involves setting the identification variable “sex” to “female”.
*Target variables*
These are the characteristics of interest, the phenomena that are being explored by means of statistical techniques.
E.g., the age of persons belonging to a particular population.
Example: Objective of the statistical investigation is to explore Berlin’s socioeconomic structure as of December 21, 1995.
The identification variables are chosen to be:

- legal: citizen
- spatial: permanent address in Berlin
- temporal: 31 December 1995

Statistical element: a registered citizen of Berlin on 31 December 1995 Population: all citizens of Berlin on 31 December 1995 Possible target variables:

Symbol | Variable | Sample space |
---|---|---|

Age (rounded to years) | ||

Sex | {female, male} | |

Marital status | {single, married, divorced} | |

Monthly income |