Data Sets

We need a way to organize statistical data.

Definition: Data Set

A data set is a multiset.

Each element of a data set represents a value that was measured for a random variable and its multiplicity is the number of times this value was measured.

Definition: (Absolute) Frequency

The (absolute) frequency of the $i$-th data point in a data set is its multiplicity.

NOTATION

$$f_i$$

Definition: Relative Frequency

The relative frequency of the $i$-th data point in a data set $S$ is the ratio of its absolute frequency to the cardinality of the data set.

$${\tilde{f}}_i\stackrel{\text{def}}{=}\frac{f_i}{|S|}$$