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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