Statistics: Definition, Functions, Scope and Limitations

In very brief:

Definition of Statistics
Statistics is the science of collection, presentation, analysis and interpretation of numerical data.

Functions of Statistics
Condensation of Data: Statistics helps in reducing the complexity of data and consequently to understand vast amount of data. Classification and tabulation are two important methods to condense data.
Facilitates Comparison: Statistics helps in comparing data obtained from different sources.Measures of central tendency, measure of dispersion, correlation coefficients, graphs etc are tools that are used for comparison.
Draw Inferences: Statistics helps in drawing inferences about a population from the analysis of a sample drawn from that population.
Testing of Hypothesis: Tests whether a statement made on a population based on the available information is valid or not.
Forecasting: Analysis of time series and regression are some of the tools that are used to predict or estimate beforehand.

Scope of Statistics:
Industry: Control charts and inspection charts.
Commerce: Stocking of material based on the estimated demand.
Agriculture: ANOVA is used in agriculture to test the equality of different population means.
Medicine: t-tests are used to test effectiveness of a new drug or compare the effectiveness of two drugs.
Economics: Index numbers, time series analysis, hypothesis testing are widely used in economics.
Planning: Statistical data related to production, consumption, demand, investment, expenditure and advanced statistical techniques are used for making policy decisions.

Limitations:
Statistics should only be used as a supportive tool in the study of a population.
Statistical laws are not exact.
It studies characteristics of population not individuals.
Not suitable for study of qualitative phenomenon. However if such phenomenon can suitable and accurately be represented in numerical form then statistical methods can be used for study.

PS: Corrections/Additions/Comments are welcome.