# Statistics

## What is a Measure?

Candidates for a job in a certain company are asked to fill out the following form:

It is clear that the data filled out by a candidate is not a substitute for a personal acquaintance with him.

The information only provides highlights concerning certain characteristics of the candidate. Based on these numbers, the company management can draw conclusions about certain characteristics of the candidate, and thereby decide whether or not to invite them to a job interview.

For example, a candidate with more than 15 years of education will generally be preferred in comparison with a candidate having only 11 years of education. The number of years of education represents a measure of the candidate’s ability to handle abstract material, their degree of motivation, etc.

On the other hand, these measures cannot provide a comprehensive indication of the candidate’s abilities. It is possible, for example, that the first candidate with more years of formal education has sufficiently poor human relations skills that it is difficult to work with them, and in that case the company may prefer to accept the second candidate. We recognize that a single measure cannot reflect the candidate’s entire range of characteristics, but measures nonetheless provide a convenient tool for comparing candidates.

## Measures of Distributions

Characteristics are not specific to job candidates, i.e., distributions also have characteristics.

In the preceding topic, we reviewed distributions relating to several variables, but we only considered the methods used to present them. We will now analyze their characteristics more thoroughly.

A measure of a distribution reflects a numerical value that expresses certain characteristics of the distribution. The measure makes it possible to learn something about the distribution by providing information that is convenient since the distribution offers a collection of data presented either as a frequency table or graphically, while a measure is only a single number derived from this data.

In this way, we can easily compare different distributions simply by comparing their respective measures.

There are two types of measures:

• Measures of Centrality
• Measures of Dispersal

What is a Measure?571