Descriptive statistics

Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. In a sense, we are using the data on members of a set to describe the set. The techniques are commonly classified as:

Graphical description in which we use graphs to summarize data.
Tabular description in which we use tables to summarize data.
Parametric description in which we estimate the values of certain parameters which we assume to complete the description of the set of data.

In general, statistical data can be described as a list of subjects or units and the data associated with each of them. Although most research uses many data types for each Unit, we will limit ourselves to just one data item each for this simple introduction.

We have two objectives for our summary:

We want to choose a statistic that shows how different units seem similar. Statistical textbooks call the solution to this objective, a measure of central tendency.
We want to choose another statistic that shows how they differ. This kind of statistic is often called a measure of statistical variability.

When we are summarizing a quantity like length or weight or age, it is common to answer the first question with the arithmetic mean, the median, or the mode. Sometimes, we choose specific values from the cumulative distribution function called quantiles.

The most common measures of variability for quantitative data are the variance; its square root, the standard deviation; the statistical range; interquartile range; and the absolute deviation.