# Statistics for SSC-CGL Tier-II (Paper-III) – Part-1

Statistics – Collection, Classification and Presentation of Statistical Data

Statistics means numerical presentation of facts.

Its meaning is divided into two forms – plural and singular.

Features of Statistics :

1. Numerically expressed
2. Affected by different factors
3. estimated or collected
4. Aggregate of facts / data
5. predetermined purpose
6. comparable
7. systematic collection

The process of collecting, classifying, presenting, analyzing and interpreting the numerical facts, comparable for some predetermined purpose are collectively known as "Statistics".

## The word statistics is used in two senses :

1. the plural sense
2. the singular sense

Plural Sense : It refers simply to statistical data or quantitative information.

Singular Sense : It refers to method or methods used in arriving at the quantitative information or dealing with it.

STATISTICAL DATA (PLURAL SENSE)

Meaning : Numerical statements of facts are statistical data. How does the statistical look like ? Table 1 is an example of statistical data. It gives information about population of India.

Characteristics :

1. Statistical data are aggregates of facts.
2. Statistical data are numerically expressed.
3. Data must be collected in a systematic manner.
4. Figures must be accurate to a reasonable degree or standard.
5. Statistics are collected for a predetermined purpose.

STATISTICAL DATA (SINGULAR SENSE)

Meaning : Using the word statistics in a singular sense means statistical methods. Statistics is a science of collection, presentation, analysis and interpretation of numerical data. These are the stages through which every statistical enquiry has to pass through. We shall discuss these stages one by one.

Stages of Statistical Enquiry

1. Collection of data.
2. Presentation of data.
3. Analysis of data.
4. Interpretation of data.

Statistics is concerned with scientific methods for collecting, organising, summarising, presenting and analysing data as well as deriving valid conclusions and making reasonable decisions on the basis of this analysis.

Statistics is concerned with the systematic collection of numerical data and its interpretation.

The word ‘ statistic’ is used to refer to

1. Numerical facts, such as the number of people living in particular area.

2. The study of ways of collecting, analysing and interpreting the facts.

Definitions by A.L. Bowley:

Statistics are numerical statement of facts in any department of enquiry placed in relation to each other. – A.L. Bowley

Statistics may be called the science of counting in one of the departments due to Bowley, obviously this is an incomplete definition as it takes into account only the aspect of collection and ignores other aspects such as analysis, presentation and

interpretation.

Bowley gives another definition for statistics, which states ‘ statistics may be rightly called the scheme of averages’ . This definition is also incomplete, as averages play an important role in understanding and comparing data and statistics provide more

measures.

Definition by Croxton and Cowden:

Statistics may be defined as the science of collection, presentation analysis and interpretation of numerical data from the logical analysis.

According to this definition there are four stages:

1. Collection of  Data: It is the first step and this is the foundation upon which the entire data set. Careful planning is essential before collecting the data. There are different methods of collection of data such as census, sampling, primary, secondary, etc., and the investigator should make use of correct method.

2. Presentation of data: The mass data collected should be presented in a suitable, concise form for further analysis. The collected data may be presented in the form of tabular or diagrammatic or graphic form.

3. Analysis of data: The data presented should be carefully analysed for making inference from the presented data such as measures of central tendencies, dispersion, correlation, regression etc.,

4. Interpretation of data: The final step is drawing conclusion from the data collected. A valid conclusion must be drawn on the basis of analysis. A high degree of skill and experience is necessary for the interpretation.

Definition by Horace Secrist:

Statistics may be defined as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

Scope of Statistics:

Statistics is not a mere device for collecting numerical data, but as a means of developing sound techniques for their handling, analysing and drawing valid inferences from them. Statistics is applied in every sphere of human activity – social as well as physical – like Biology, Commerce, Education, Planning, Business Management, Information Technology, etc. It is almost impossible to find a single department of human activity where statistics cannot be applied. We now discuss briefly the applications of statistics in other disciplines.

Statistics and Industry:

Statistics is widely used in many industries. In industries, control charts are widely used to maintain a certain quality level. In production engineering, to find whether the product is conforming to specifications or not, statistical tools, namely inspection plans, control charts, etc., are of extreme importance. In inspection plans we have to resort to some kind of sampling – a very important aspect of Statistics.

Statistics and Commerce:

Statistics are lifeblood of successful commerce. Any businessman cannot afford to either by under stocking or having overstock of his goods. In the beginning he estimates the demand for his goods and then takes steps to adjust with his output or purchases. Thus statistics is indispensable in business and commerce.

As so many multinational companies have invaded into our Indian economy, the size and volume of business is increasing.  On one side the stiff competition is increasing whereas on the other side the tastes are changing and new fashions are emerging. In this connection, market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.

Statistics and Agriculture:

Analysis of variance  (ANOVA) is one of the statistical tools developed by Professor R.A. Fisher, plays a prominent role in agriculture experiments. In tests of significance based on small samples, it can be shown that statistics is adequate to test the significant difference between two sample means. In analysis of variance, we are concerned with the testing of equality of several population means.

For an example, five fertilizers are applied to five plots each of wheat and the yield of wheat on each of the plots are given. In such a situation, we are interested in finding out whether the effect of these fertilisers on the yield is significantly different or not.

In other words, whether the samples are drawn from the same normal population or not. The answer to this problem is provided by the technique   of ANOVA and it is used to test the homogeneity of several population means.

Statistics and Economics:

Statistical methods are useful in measuring numerical changes in complex groups and interpreting collective phenomenon. Nowadays the uses of statistics are abundantly made in any economic study. Both in economic theory and practice, statistical methods play an important role.

Alfred Marshall said, “ Statistics are the straw only which I like every other economist have to make the bricks”. It may also be noted that statistical data and techniques of statistical tools are immensely useful in solving many economic problems such as wages, prices, production, distribution of income and wealth and so on. Statistical tools like Index numbers, time series Analysis, Estimation theory, Testing Statistical Hypothesis are extensively used in economics.

Statistics and Education:

Statistics is widely used in education. Research has become a common feature in all branches of activities. Statistics is necessary for the formulation of policies to start new course, consideration of facilities available for new courses etc. There are many people engaged in research work to test the past knowledge and evolve new knowledge. These are possible only through statistics.

Statistics and Planning:

Statistics is indispensable in planning. In the modern world, which can be termed as the “world of planning”, almost all the organisations in the government are seeking the help of planning for efficient working, for the formulation of policy decisions and execution of the same.

In order to achieve the above goals, the statistical data relating to production, consumption, demand, supply, prices, investments, income expenditure etc and various advanced statistical techniques for processing, analysing and interpreting such complex data are of importance. In India statistics play an important role in planning, commissioning both at the central and state government levels.

Statistics and Medicine:

• In Medical sciences, statistical tools are widely used. In order to test the efficiency of a new drug or medicine, t – test is used or to compare the efficiency of two drugs or two medicines, t-test for the two samples is used. More and more applications of statistics are at present used in clinical investigation.

Statistics and Modern applications:

Recent developments in the fields of computer technology and information technology have enabled statistics to integrate their models and thus make statistics a part of decision making procedures of many organisations. There are so many software packages available for solving design of experiments, forecasting simulation problems etc.