Statistical inference is the theory, methods, and practice of forming judgments about the parameters of a population and the reliability of statistical relationships, typically on the basis of random sampling.
Probability theory the branch of mathematics that deals with quantities having random distributions.
Nominal data is 
 used for labeling variables, without anyquantitative value.  “Nominal” scales could simply be called “labels.” 
Ordinal data is 
the order of the values is what’s important and significant, but the differences between each one is not really known.
Interval data is 
numeric scales in which we know not only the order, but also the exact differences between the values.
Ratio data is 
the ultimate nirvana when it comes to measurement scales because they tell us about the order, they tell us the exact value between units, and they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied.