Random variables are characteristics of the observational units which can have different possible values (this is the practical, not the statistical definition)
There are two different types of random variables:
Quantitative (numerical, measurement) variables represent an amount or quantity of something (e.g. time spent waiting for the bus)
Qualitative (categorical) variables represent things that can be categorized (e.g. the colors of the cars that pass while you wait for the bus)
Letters like X or Y represent random variables if its value is not known before the experiment is run.
How about our example? The price of the apartment? Or, location of the apartment?
Quantitative: Discrete vs. Continuous
Discrete random variables can only take on values from a countable set of numbers such as the integers or some subset of integers. (Usually, they can’t be fractions.)
Continuous random variables can take on any real number in some interval. (They can be fractions.)
Note: We consider variables like height to be continuous even though we can only measure them in discrete units (e.g. millimeters).
Categorical: Nominal vs. Ordinal
Nominal (unordered) random variables have categories where order doesn’t matter.
Ordinal (ordered) random variables have ordered categories. ( e.g. grade levels, income levels, school levels, ...)
Explanatory vs. Response Variable
The explanatory variable attempts to explain (or is purported to cause) differences in a response variable (or outcome variable), (e.g. homework scores and exam scores can be explanatory variables for the final grade).
But in order to make inferences from a sample to a population the sample needs to be representative. How do we insure that? RANDOMIZATION!!