# What is discrete and continuous in math

## Discrete and Continuous Random Variables    Next page:Analysis categorical and continuous Upwards:Types of variables Previous page:Quantitative and qualitative variables & nbsp index

From the point of view of mathematical statistics, there are two types of variables: discrete and continuous "random variables". :
• Discreet Random variables either have a finite number or a countably infinite number of characteristics. The set of natural numbers is sufficient to name their characteristics. Depending on the number of manifestations, one also speaks of dichotomous (2), trichotomes (3), polytomes (finite number ) or from Counting variables (infinite number of expressions).
• At continuous Random variable is between two values also every intermediate value in the interval is possible, no matter how small this interval is. To name their characteristics, the set of rational numbers is necessary (e.g. decimal fractions with an infinite number of decimal places).
Both definitions describe exclusively mathematical properties of both types of variables, which is completely sufficient for mathematical statistics because it deals with the formal description of (hypothetical) "random experiments" (hence the name Coincidencevariable). This distinction is important for applied statistics because mathematical statistics have developed different "distribution models" for discrete and continuous random variables that can be used for the statistical analysis of real phenomena. It is obvious, however, that these (theoretical) models cannot simply be transferred to real phenomena.    Next page:Analysis categorical and continuous Upwards:Types of variables Previous page:Quantitative and qualitative variables & nbsp index HJA 2001-10-01