Notes On Statistics - the study of collecting, organizing, and interpreting data.

Meaning And Definition of Statistics:

        The word Statistics refers to either quantitative information or to a method of dealing with quantitative informations.

        In the opinion of Webster, statistics is defined as, "the classified facts representing the condition of the people in a state especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement".

        In the word of Yule and Kendall, "By Statistics we mean quantitative data affected to a marked extent by multiplicity of causes."

Characteristics of Statistics:
  1. Statistics are aggregates of facts. Single or isolated figures are not statistics for the simple reason that such figures cannot be compared.
  2. Statistics are numerically expressed. Qualitative statements are considered vague and one cannot draw any conclusion from them.
  3. Statistics are collected in a systematic manner with a suitable plan
  4. Statistics are collected for a pre determined and specific purpose
Stages of Statistical Investigation:
  1. Collection of data
  2. Organization of data
  3. Presentation of data
  4. Analysis of data
  5. Interpretation of data
Functions Of Statistics:
  1. It presents the facts in a definite form
  2. It simplifies the mass of figures
  3. It facilitates comparison
  4. It helps in formulating and testing hypothesis
  5. It helps in prediction
  6. It helps in formulating suitable policies
Statistics - Science Or Art:

        It is a matter of debate, whether Statistics-Science Or Art. Statistics is both a science and an art. It can be described as science but not a pure science like physics or chemistry because statistical phenomenon is generally affected by a multiplicity of causes which cannot always be measured accurately. In other words, the science of statistics by its nature is less precise than the natural science. More appropriately, statistics may be regarded as a scientific method because it is really a tool which can be used in scientific studies. It is also considered as science because its methods are basically systematic and have general application

        If science is knowledge, then art is action. Looking from this angle Statistics can be regarded as an art. It involves the application of given method to obtain facts, derive results and finally use them for appropriate action. It can also be described as an art because their successful application depends to a considerable degree, on the skill and special experience of a statistician and of the knowledge of the field of application.

Scope Of Statistics:

        The scope of statistics is so vast and ever expanding that not only it is difficult to define it but also not wise to do so. Statistics pervades all subject matter- its use has permeated almost every facet of our lives. It is a tool of sciences indispensable to search and intelligent judgment and has become a recognized discipline in its own right. There is hardly any field be it trade or commerce, economics, physics, chemistry, astronomy etc. the application of statistics is so vast that it is often remarked as a "Statistics is what statistician do"

Significance of Statistics In Economics:

        In the year 1890, Prof. Alfred Marshall opined that "Statistics are the straw out of which I, like every other economists, have to make bricks". Statistical data and statistical methods are of immense help in the proper understanding of economic problems and in the formulation of economic policies.

        The significance of statistics in economics is as follows:

  1. Statistics helps in the measurement of national product and input-output analysis.
  2. Statistics helps in the study of business cycle and business fluctuations.
  3. Statistical surveys helps in studying the theories of prices, price trends and pricing policies.
  4. Operational studies of public utilities require both statistical and legal tools of inflation.
  5. Statistics helps in solving various economic problems such as poverty, unemployment, uneven distribution of income and wealth.
Limitations of Statistics:
  1. The study of individual measurement lies outside the scope of statistics.
  2. Statistics deals with only the quantitative characteristics neglecting the qualitative aspects.
  3. Statistics is only a method of studying a problem and does not provide any solution to the problem.
  4. The conclusion obtained statistically is not universally true. But are true only certain circumstances.
  5. The greatest limitation of statistics is that it can be misused due to several reasons. Statistics are like clay and can be molded in any manner in order to obtained desired conclusion.
Meaning Of Statistical Survey:

        Statistical Surveys are the most popular device for obtaining desired data. A statistical survey is the process of collecting data from existing population units with no particular control over factor that may affect the population characteristics of the interest in the study.

        For example, the study of salary of workers in a factory may reveal informations about the workers' salary. But the salary of the workers are determined by a number of factors such as age, experience, nature of job, level of education etc. But statistical survey has no control over these factors.

        A statistical survey may be either a general survey or special survey. The population census is the best of general survey and special surveys are those that are conducted to obtain data for analyzing and finding solution for a particular problem. A special survey passes the stages of planning the survey and execution of the survey.

Meaning And Requisites Of Statistical Unit:

        The unit in terms of which the investigator counts or measures the variables or attributes selected for enumeration, analysis and interpretation, is known as statistical unit.

        While fixing the statistical unit for an enquiry, it is useful to consider the following points:

  1. The unit must suit the purpose of enquiry.
  2. It should be simple to understand.
  3. It should be specific.
  4. The unit selected should be a stable character.
  5. The unit selected should be comparable.
Meaning of Primary Data:

        Primary data are those data that are collected by the investigator at the first hand. A primary source is one that itself collects the data. Primary data are obtained by a study specifically designed to fulfill the data needs of the problem at hand. Such data are original in character and are generated through large number of surveys.

What Are The Sources Of Collection Of Data:

1. Primary Source:

        A primary source is one that itself collects the data.

2. Secondary Source:

        A secondary source is one that makes available data which were collected by some other agency.

Meaning of Secondary Data:

        Secondary data are those data that are collected by the investigator from published or unpublished sources. A secondary source is one that makes available data which were collected by some other agency. The secondary data constitute the chief material on the basis of which statistical work is carried in many investigations.

Difference Between Primary Data And Secondary Data:

        The difference between primary and secondary data is only of degree. Data which are primary in the hands of one becomes secondary in the hands of another. Data are primary for the institution or agency collecting them. But for the rest of the world, it becomes secondary.

Choice Between Primary Data And Secondary Data:

        The investigator must decide at the outset whether he will use primary date or secondary data in an investigation. The choice between primary data and secondary data depends mainly on the following consideration.

  1. Nature and scope of enquiry.
  2. Availability of financial resources.
  3. Availability of time.
  4. Degree of accuracy required.
  5. The collecting agency- whether individual or an institution or Government body.
Methods Of Collection Of Primary Data:

The different methods of collection of primary data are:

  1. Direct personal Interview.
  2. Indirect oral interviews.
  3. Informations from Correspondents.
  4. Mailed questionnaire method.
  5. Schedules sent through enumerators.
Description Of the Methods Of Collection Of Data:

1. Direct Personal Interview:

  strong;      In this method, the investigator himself collects the required informations on the basis of face to face contact with the person from whom the information is to be obtained.

2. Indirect Oral Interview:

        Under this method, the information is collected indirectly and thereby a small list of questions relating to the enquiry is prepared and put to different persons and their answers are recorded are recorded systematically.

3. Informations Form Correspondents:

        Under this method, the investigator appoints local agents or correspondents in different places to collect informations. These correspondents collect and transmit the informations to the central office where the data are processed.

4. Mailed Questionnaire Method:

        Under this method, a list of questions pertaining to the survey are prepared and sent to different informants by post with a request to fill up the questionnaire and send it back within a specific time frame.

5. Schedule Sent Through Enumerators:

        Under this method, the enumerator contacts the informants; gets reply to the questions contained in the schedule and fill them in their own handwriting in the questionnaire form. The essential difference between the mailed questionnaire method and this method is that whereas in the former, the questionnaire is sent to the informants by post, in the latter, the enumerator carry the questionnaire personally to the informants.

Meaning of Secondary Data:

        Secondary data are those data that are collected by the investigator from published or unpublished sources. A secondary source is one that makes available data which were collected by some other agency. The secondary data constitute the chief material on the basis of which statistical work is carried in many investigations.

Methods Of Collection Of Secondary Data:

The different methods of collection of data are as follows:

  1. Official publications of various governments-Central, State, Local Bodies
  2. Official publications of various foreign governments and international bodies like IMF, World Bank
  3. Reports and publications of trade associations, banks, Chambers Of Commerce, Stock Exchange, etc
  4. Technical Trade journals like Economies, Indian Journal Of Economies.
  5. Report submitted by economists, educational institutions, research scholars.
Difference Between Primary Data And Secondary Data:

        The difference between primary and secondary data is only of degree. Data which are primary in the hands of one becomes secondary in the hands of another. Data are primary for the institution or agency collecting them. But for the rest of the world, it becomes secondary.

Meaning And Process Of Sampling:

        Simply, sampling is the process of studying about the population on the basis of a sample drawn from it. Thus in sampling technique, instead of every unit of the aggregate only a part of the aggregate is studied and the conclusions are drawn on that basis for the entire aggregate.

        The process of sampling involves the following:

  1. Selecting the sample.
  2. Collecting the informations.
  3. Making an inference about the population.
Essentials Of Sampling:

        Sampling, to be worthy or meaningful must possess the following essentials:

  1. A sample selected should be such that represents the aggregate otherwise the result obtained may be misleading.
  2. The size of the sample should be adequate.
  3. The selected items should be independent of each other and should have the same chance of being selected in the sample.
  4. The sample selected should be homogeneous.
Methods of Sampling:

        The various methods of sampling can be grouped into two broad groups:

  1. Probability Sampling (Random Sampling)
  2. Non-Probability Sampling (Non- Random Sampling)
1. Probability Sampling (Random Sampling):

        Probability Sampling methods are those in which every item in the aggregate has a fair chance of being chosen in the sample. The selection process is independent of the person making the study.

2. Non-Probability Sampling (Non- Random Sampling):

        Non-probability sampling methods are those which do not provide every item in the aggregate with a known chance of being selected in the sample. The selection process is, at least, partially subjective.

Difference Between Random And Non-Random Sampling:

        The significant difference between random and non-random sampling is that whereas the pattern of sampling variability can be ascertained in case of random sampling, in non-random sampling, there is no way of knowing the pattern of variability in the process.

Sources Of Data:

        The two main sources of data are:

1. Internal Sources:

        The internal sources of date are those which are obtained from the internal reports of the organization. A large number of individual organizations and government departments generate internal data as their regular function.

2. External Sources:

        External sources refer to those informations collected from other sources. They can be collected from primary as well as secondary sources.

Sources of secondary Data:

        The major sources of secondary data can be classified into two:

I. Published Sources:

        It includes all sources of published informations including:

  1. Reports and official publications of IMF, World Bank, Central and State Government, etc
  2. Semi-Official publications of various local bodies such as Municipal Corporations District Boards etc.
  3. Publications of autonomous and private institutes such as Federation Of Indian Chambers Of Commerce and Industry, Institute of Chartered Accountants, etc

II. Unpublished Sources:

        All statistical material is not always published. There are various sources of unpublished data such records maintained by various government and private offices, studies made by research institutions, scholars etc. can be a good unpublished source of secondary data.

Merits And Demerits Of Sampling Method:


  1. Sampling is less time consuming as because sampling studies the part of the population
  2. Sampling is less expensive than census method as because only a part of the population is studied
  3. The results obtained from sampling method is more reliable than from a complete count because it is possible to determine the sampling errors (if any)
  4. It is possible to collect detailed information under this method since the technique save time and money
  5. Finally, sampling method is used to judge the accuracy of the information on the census basis.


  1. Sampling method should be very carefully planned and executed so as to obtain accurate result. Otherwise it may be misleading.
  2. Sampling requires expert hands. In the absence of qualified and experienced personnel sampling method cannot be executed.
  3. Sampling at times becomes complicated and time consuming if information is required to be taken for each and every unit under study. This is because in such cases, complete enumeration survey becomes necessary.
Size of Sample:

        The size of a sample is a matter of great concern and is an important decision that needs to be taken at the time of adopting a sampling technique. The size of sample means the number of sampling units selected from the population of investigation. Different experts have expressed different opinions regarding the size of sample. If the size of the sample is too small, it may not represent the universe and the inference drawn may be misleading. On the other hand, is the size of the sample is large, it may impose financial burden and may be time consuming. Hence, the size of the sample should be optimum.

        In the opinion of Parten, optimum size is one that fulfils the requirements of efficiency, representativeness, reliability and flexibility.

        The following factors should be considered while deciding the size of sample.

  1. The size of the universe.
  2. The availability of resources.
  3. The required degree of accuracy or precision.
  4. Homogeneity or heterogeneity of the universe.
  5. Nature of study.
  6. Technique adopted.
  7. Nature of respondents.

        The above mentioned factors should be weighted before arriving at the sampling size.