Statistical parameters are mathematical properties of a set of numerical values. These are typically real numbers (integers are converted into reals). The following symbolic conventions are established:

• The numerical values are conventionally represented by x, which actually represents the variable of which the numerical values are values.
• A particular value out of the set is xi.
• The cardinality of the set is conventionally designated by n.
• If the set is taken as a list, this starts with x1, extends over all the xi and ends with xn.

In empirical sciences, the numerical values are typically properties of individuals in a sample that has been taken to represent a population. The values may have been measured or determined otherwise. In statistical calculations, a set of values is typically arranged in a column of a table. The pattern of these values in the sample is also called a distribution. The parameters are used to describe the distribution succinctly; they are like a summary of the set of the values.

The following three are the most elementary statistical parameters:

• mean
• standard deviation
• standard error

In empirical sciences, a distribution of numerical values is generally characterized by quoting two statistical parameters: the arithmetic mean and the standard deviation. To describe a normal distribution, these two are sufficient.

There are also statistical parameters applying to the population that the sample has been taken from. In contrast to the statistical properties of a sample, these are of necessity estimations.