Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data. Some statistical measures include mean, regression analysis, skewness, kurtosis, variance and analysis of variance.

Statistics is a term used to summarize a process that an analyst uses to characterize a data set. If the data set depends on a sample of a larger population, then the analyst can develop interpretations about the population primarily based on the statistical outcomes from the sample. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form.

Statistical methods analyze large volumes of data and their properties. Statistics is used in various disciplines such as psychology, business, physical and social sciences, humanities, government and manufacturing. Statistical data is gathered using a sample procedure or other method. Two types of statistical methods are used in analyzing data: descriptive statistics and inferential statistics. Descriptive statistics are used to synopsize data from a sample exercising the mean or standard deviation. Inferential statistics are used when data is viewed as a subclass of a specific population.

**Importance and Scope of Statistics**

**(i) Statistics in Planning**

Statistics is indispensable in planning—may it be in business, economics or government level. The modern age is termed as the ‘age of planning’ and almost all organizations in the government or business or management are resorting to planning for efficient working and for formulating policy decision.

To achieve this end, the statistical data relating to production, consumption, birth, death, investment, income are of paramount importance. Today efficient planning is a must for almost all countries, particularly the developing economies for their economic development.

**(ii) Statistics in Mathematics**

Statistics is intimately related to and essentially dependent upon mathematics. The modern theory of Statistics has its foundations on the theory of probability which in turn is a particular branch of more advanced mathematical theory of Measures and Integration. Ever increasing role of mathematics into statistics has led to the development of a new branch of statistics called Mathematical Statistics.

Thus Statistics may be considered to be an important member of the mathematics family. In the words of Connor, “**Statistics is a branch of applied mathematics which specializes in data**.”

**(iii) Statistics in Economics**

Statistics and Economics are so intermixed with each other that it looks foolishness to separate them. Development of modern statistical methods has led to an extensive use of statistics in Economics.

All the important branches of Economics—consumption, production, exchange, distribution, public finance—use statistics for the purpose of comparison, presentation, interpretation, etc. Problem of spending of income on and by different sections of the people, production of national wealth, adjustment of demand and supply, effect of economic policies on the economy etc. simply indicate the importance of statistics in the field of economics and in its different branches.

Statistics of Public Finance enables us to impose tax, to provide subsidy, to spend on various heads, amount of money to be borrowed or lent etc. So we cannot think of Statistics without Economics or Economics without Statistics.

**(iv) Statistics in Social Sciences**

Every social phenomenon is affected to a marked extent by a multiplicity of factors which bring out the variation in observations from time to time, place to place and object to object. Statistical tools of Regression and Correlation Analysis can be used to study and isolate the effect of each of these factors on the given observation.

Sampling Techniques and Estimation Theory are very powerful and indispensable tools for conducting any social survey, pertaining to any strata of society and then analyzing the results and drawing valid inferences. The most important application of statistics in sociology is in the field of Demography for studying mortality (death rates), fertility (birth rates), marriages, population growth and so on.

**(v) Statistics in Trade**

As already mentioned, statistics is a body of methods to make wise decisions in the face of uncertainties. Business is full of uncertainties and risks. We have to forecast at every step. Speculation is just gaining or losing by way of forecasting. Can we forecast without taking into view the past? Perhaps, no. The future trend of the market can only be expected if we make use of statistics. Failure in anticipation will mean failure of business.

Changes in demand, supply, habits, fashion etc. can be anticipated with the help of statistics. Statistics is of utmost significance in determining prices of the various products, determining the phases of boom and depression etc. Use of statistics helps in smooth running of the business, in reducing the uncertainties and thus contributes towards the success of business.

**(vi) Statistics in Research Work**

The job of a research worker is to present the result of his research before the community. The effect of a variable on a particular problem, under differing conditions, can be known by the research worker only if he makes use of statistical methods. Statistics are everywhere basic to research activities. To keep alive his research interests and research activities, the researcher is required to lean upon his knowledge and skills in statistical methods.

**Limitations of Statistics**

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Statisticians improve the quality of data with the design of experiments and survey sampling.

**(i)** Statistics does not deal with isolated measurement

**(ii)** Statistics deals with only quantitative characteristics

**(iii)** Statistics laws are true on average. Statistics are aggregates of facts. So single observation is not a statistics, it deals with groups and aggregates only.

**(iv)** Statistical methods are best applicable on quantitative data.

**(v)** Statistical cannot be applied to heterogeneous data.

**(vi)** It sufficient care is not exercised in collecting, analyzing and interpretation the data, statistical results might be misleading.

**(vii)** Only a person who has an expert knowledge of statistics can handle statistical data efficiently.

**(viii) **Some errors are possible in statistical decisions. Particularly the inferential statistics involves certain errors. We do not know whether an error has been committed or not.

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