Introduction to Statistics

What is Statistic?

  • Statistics has been defined differently by different authors and each author has assigned new limits to the field which should be included in the scope of statistics
  • Seligman, defines “Statistics is a science which deals with the method of collecting, classifying, presenting, comparing and interpreting the numerical data to throw light on enquiry.
  • Horace Secrist defines “Statistics as the aggregate of facts affected to mark extent by the multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner for the predetermined purpose and placed in relation to each other”.
  • Prof. Boddington defined “Statistics as the science of estimates and probabilities”.
  • Croxton and Cowden define “ Statistics is the science of collection, presentation, analysis, and interpretation of numerical data from logical analysis”.
  • A.L. Bowley defines, “Statistics may be called the science of counting and may be called the science of averages”.
  • According to King, “The science of statistics is the method of judging collective, natural or social, the phenomenon from the results obtained from the analysis or enumeration or collection of estimates”.
    We can see that the definition given by Boddington is complete and covers all characteristics of Statistics.

Components of Statistics:

  • Collection of Data
  • Presentation of Data
  • Analysis of Data
  • Interpretation of Data:

Importance of Statistics in Business and Management:


  • Statistical sampling techniques are used during the conduction of audits for clients. It also helps in detecting the trend and make projection for next year.

Finance and Investments:

  • Statistical information can be used to study the trend in securities and that can be used to provide investment recommendations. Statistical methods help in selecting securities which are safe and have the best prospects of yielding a good income.


  • Statistical analysis is frequently used in for making a decision in the field of marketing it is the first step to find out what can be sold and to whom. Then using statistical methods a suitable strategy is formulated. A statistical analysis of data on production purchasing power, man power, habits of competitors, habits of consumer, transportation cost can be done before entering a new market.
  • Nowadays electronic scanners at retail checkout counters are used to collect data and to study buying behavior of the customer. The data obtained in this procedure is used to analyze it to formulate future marketing policies.


  • Statistical methods are used in quality control during the production process. It is also used to control and manage the flow of production. Statistical methods are used in scheduling of men and machines.


  • Statistical data gathering and analysis of the information, help banks in their own business and also give an idea of the general economic situation of every segment of business in which they may have interest. Using this analysis they can formulate their lending policies.


  • The management control process combines statistical and accounting method in making the overall budget for the coming year including sales, materials, labor and other costs and capital requirement.


  • Purchase department can fix their schedule of purchasing orders depending upon the trends in consumption of raw materials and inputs. Thus they decide what to buy? When to buy? And how much to buy?


  • Statistical techniques and analysis are used for forecasting the future of the economy. Time series like moving averages, indicators like inflation index are statistical methods. We can consider statistics as the backbone of economics.

Categories of Statistics:

  • Statistics is broadly categorized into two parts based on their functions a) Descriptive Statistics and b) Inferential Statistics

Descriptive Statistics:

  • Descriptive Statistics involves collecting, organizing, summarizing and presenting data.
  • It is useful in clinical research, while communicating the results with experiments.
  • The methods used in this statistics is preparing tables, drawing graphs, measuring central tendency and the variation of the data from the central value.

Inferential Statistics:

  • Inferential Statistics involve making inference, hypothesis testing, relation determination and making predictions.
  • The data obtained in descriptive statistics is analyzed and a valid inference is made out of it for effective decision making for managers and professionals. In this type deductions and conclusions are made regarding the population under study by collecting a sample from the population.

Characteristics of Statistics:

Statistics are aggregate of facts:

  • A single figure cannot be analyzed. A single figure relating to height, production, sales, birth, death etc. cannot be called statistics, but aggregates of such figures like height of students in a class, production of different models of cars in last fiscal year, can be considered as statistics because of their comparability, variation,  and relationship.

Statistics are affected by great extent by a multiplicity of causes:

  • A number of causes affect statistics in a particular field of enquiry, e.g., in yield of crops statistics are affected by climate, soil, fertility, availability of raw materials, rain fall, the quality of seeds used, quality and quantity of fertilizers used and methods of  transport.

Statistics are numerically expressed:

  • Statistics is concerned essentially with facts expressed in numerical form with their quantitative details but not qualitative descriptions. Therefore, facts indicated by terms such as ‘good’, ‘poor’ are not statistics unless a numerical value, is assigned to each expression. For example we can state “Demand increases, price increases”. Statistics do not trust such statement without proper numerical data to prove it.

Statistics are enumerated or estimated with required degree of accuracy:

  • Absolute accuracy is neither necessary nor sometimes possible in social sciences. But whatever standard of accuracy is once adopted, should be used throughout the process of collection or estimation. In statistics the data is collected from field or estimated with proper degree of accuracy.
  • The degree of accuracy depends on the purpose of the study. The average height of students in a class is measured in centimeter where accuracy is not that important, but the length of screw used in automobile is measured in millimeter because accuracy is important in this case.

Statistics should be collected in a systematic manner for a predetermined purpose:

  • The required fact should be collected with planning and with suitable scientific methods. If it is not done scientifically and properly it may give wrong or misleading inferences.  If there is no predetermined purpose, all the efforts in collecting the figures and collection of indiscriminate data may be waste of time and resources.

Statistics should be capable of being placed in relation to each other:

  • The collected figure should be comparable and well-connected so that analyzation of the collected data is possible. Thus in statistics similar related quantities should be compared.

Functions of Statistics:

To present facts in a definite form:

  • Without a statistical study our ideas are likely to be vague, indefinite and hazy, but figures helps as to represent things in their true perspective. Using statistics we can collect and organize data. Using organize data its analysis is carried out to verify the fact.

To simplify unwieldy and complex (mass) data:

  • Statistical methods reduce complexity of data by choosing proper sample. Studying the sample and applying statistical method to this sample, the huge and complex mass data can be understood. The complex data may be simplified by presenting them pictorially in the form of a tables, graphs or diagrams, or representing it through averages and variations.

To use it for comparisons:

  • The purpose of data collection can be fulfilled only when they are compared with others of the same type. To do this certain statistical methods, such as average, coefficients, rates, ratios, grand totals, variations, measure of dispersion etc. are used.

To bring out trends and tendencies in data:

  • The data is collected and organized, then using techniques like moving averages, time series, interpolation and extrapolation the trend can be studied which is useful for forecasting.

To provide guidance in the formulation of policies and take decision:

  • Government and businesses used statistics to take decision by analyzing the data. Managers can used statistical techniques to arrive at a decision and can support it with necessary statistical data.

To enlarge individual experience:

  • The knowledge collecting ability of human being is limited to its senses. The knowledge can extended in various ways by studying certain conclusions and results, using certain statistical techniques.  Statistics bring hidden relation between variables.

To enable measurement of the magnitude of a phenomenon:

  • Using statistical techniques we can estimate the population of the country, the rate at which it is growing, the quality of life, their standard of living, their consumption patter, their disposable incomes. We can also estimate production of food grains.

Limitations of Statistics:

The use of statistics is limited numerical studies:

  • Statistical methods cannot be applied to study the nature of all type of phenomena. It deals with only such phenomena those can be measured quantitatively and to whom a numerical value can be assigned. For, example, the health, poverty, and intelligence, beauty of a group of individuals, cannot be quantitatively measured, and hence cannot be part of a statistical study. Thus statistics does not deal with qualitative data.

Statistics does not deal with individual facts:

  • Statistical methods deal with population or aggregate of individuals rather than with individuals. Analysis of individual fact without comparison is highly difficult.

Statistical relies on estimates and approximations:

  • Statistical laws are not exact laws like mathematical or chemical laws. Statistical laws are true only on averages. They are derived by taking a majority of cases and are not true for every individual. Thus they are probabilistic and hence the statistical inferences are uncertain.

Statistical results might lead to fallacious or wrong conclusions:

  • By deliberate manipulation of figures and unscientific handling or due to prejudice on part of data collectors (enumerators. Lack of scientific methods and statistical methods can create such incorrect data. Such manipulated or incorrect data placed in the hands of an expert may lead to fallacious results. The figures may be stated without their context or may be applied to a fact other than the one to which they really relate.

Statistical Softwares:

  • If collected data is small the data can be classified, organized easily and inference can be obtained in short period. But if data collected is large then we have to take examples of softwares.
  • Softwares used in statistics are Minitab, SPSS (Statistical Package for Social sciences and E-views.

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