Descriptive statistics

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. It is distinguished from inferential statistics which is also known as inductive statistics, in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that it is, unlike inferential statistics, are not developed on the basis of probability theory. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented.

For example in a paper reporting on a study involving human subjects, there typically appears a table giving the overall sample size, sample sizes in important subgroups and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, and the proportion of subjects. Descriptive statistics is also a set of brief descriptive coefficients that summarizes a given data set that represents either the entire population or a sample.

Descriptive statistics provides simple summaries about the sample and about the observations that have been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

In the business world, Descriptive statistics provide a useful summary of security returns when performing empirical and analytical analysis, as they provide a historical account of return behavior. Although past information is useful in any analysis, one should always consider the expectations of future events.

The major analysis of Descriptive statistics consists of two analysis which are Univariate and Bivariate analysis.

Univariate analysis

Univariate analysis involves describing the distribution of a single variable, including its central tendency including the mean, median, and mode and dispersion including the range and quantiles of the data-set, and measures of spread such as the variance and standard deviation. 

Bivariate analysis

When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables. In this case, descriptive statistics include:

Ø Cross-tabulations and contingency tables

Ø Graphical representation via scatter plots

Ø Quantitative measures of dependence

Ø Descriptions of conditional distributions

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