# Statistical variable

In the statistical and empirical one assigns statistical variable or a statistical characteristic of a survey unit ( examination unit ) an expression to.

A statistical variable is present if the characteristics of certain characteristics can be expressed by a number or by number intervals (values ​​of the variables ) and these values include empirically measurable frequencies .

## Systematics

Population: Development of the German WP
Characteristic carriers: Development status (date)
Characteristic: Number of existing articles
Characteristic value: 1, 2, ..., 1,000,000, ...

Population ( population )

Feature carrier ( investigation unit , survey unit )
Characteristic ( statistical variable )
Characteristic value ( value of the variable)

Examples:

• Population : residents of city X
Characteristic carrier: a resident
Feature: gender
Characteristic expression: male
• Population: days of a study period
Characteristic carrier: one day
Feature: amount of precipitation in Germany
Characteristic expression: 1.5 cubic kilometers

## Classification of features

Features can have different scale levels . In principle, a distinction can be made between quantitative characteristics that can be measured on a metric scale (such as body weight or income) and qualitative characteristics (such as gender or color). In the second case, one also speaks of a categorical characteristic , since characteristics are given in the form of a category .

## Statistical variable vs. Random variable

They are two sides of a variable and they define the same characteristics. Behind a statistical variable, however, there is a population or a sample and the relative and absolute frequencies associated with the characteristics. Behind a random variable is a random experiment (model) and, associated with the characteristic values, probabilities.

Example (choice):

Random variable
There is a predetermined probability that a party will be elected. The random variable : party elected has two possible characteristics: party elected or party not elected . The probability that the party will be elected and the probability that the party will not be elected is .${\ displaystyle \ pi}$${\ displaystyle X}$${\ displaystyle \ pi}$${\ displaystyle 1- \ pi}$
Statistical variable
There are from voters who voted for the party. The statistical variable : party elected has two possible values: party elected or party not elected . The relative frequency with which the party is elected, and that at which the party was not elected .${\ displaystyle p}$${\ displaystyle n}$${\ displaystyle X}$${\ displaystyle p / n}$${\ displaystyle 1-p / n}$

## literature

• Rainer Schlittgen : Introduction to Statistics. 9th edition. Oldenbourg Wissenschaftsverlag, Oldenbourg 2000, ISBN 3-486-27446-5
• Peter Bohley: Statistics - Introductory textbook for economists and social scientists. 6th edition. Oldenbourg Wissenschaftsverlag, Oldenbourg 1996, ISBN 3-486-23497-8