Basically, there are two main divisions of statistics called theoretical statistics and applied statistics.
Theoretical statistics deals with the formulation of general principles, devices and rules which are used in statistical work. Theoretical statistics is mathematical in nature and its rules are used in descriptive as well as inferential statistics.
Applied Statistics deals with the application of the statistical methodology and general rules in the investigation of a specific problem. Its study falls in business, economics, demography, agriculture, market research, banking etc. e.g., the index number of prices helps to see the changes in the level of prices, which is important for consumers, producers and the government. The descriptive and Inferential Statistics arise from Applied Statistics.
Statistical methods categorize into two major areas called descriptive statistics and inferential statistics.
Descriptive Statistics OR Deductive Statistics:
Descriptive statistics is that branch of statistics which deals with those methods concerned with collecting and describing a set of data so as to yield meaningful information.” or “Statistics which summarizes, presents, analysis the statistical data is called Descriptive Statistics”.
It covers the condensation of data, graphic presentations and salient features of data, which provides information about the center and spread of the observations. The construction of tables, graphs, charts and other relevant computations in various newspapers and magazines usually fall in the area categorized as descriptive statistics.
Inferential Statistics OR Inductive Statistics:
“Statistical inference comprises those methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data.” or “Statistics which provide valid conclusions about the population parameters along with an extent of their reliability on the basis of a sample data.”
It is very important branch of statistics based on probability theory used to make the inferences about the population on the basis of sample. So, this includes the estimation of population parameter and testing of hypothesis.
This phase of statistics is based on probability theory as the inference which are made on the basis of sample evidence, cannot be absolutely certain.