Title Unit 1 Introduction to Statistics.pdf ✅

1.1 Introduction Statistics is not a new discipline. The origin of statistics had been started with the origin of the development of human society. It is as old as the human society as human beings used statistics even unknowingly in preliminary phase of development of human civilization. In ancient time, statistics was regarded as the science of statecraft and it was used to collect the data of age and sex-wise population as well as property and wealth of state by the governments for framing military and fiscal policies. The historical evidences such as census of population during the construction of 'Pyramid' in Egypt by Pharaohs, the counting and recording of losses occurred during Napoleonic war in Britain, censuses held in England and Germany in the middle ages are regarded as the initiation of development of statistics. But nowadays it embraces almost each and every sphere of natural and human activity. By the works of French gambler Chevalier de-Mere (Science of Probability), De-Moivre (Normal Probability), Gauss (Principle of Least Square and Normal Laws of Errors), Markov (Markov chains), Liapounoff (Central Limit Theorem) etc have made the outstanding contributions to modernize statistics. Similarly, Francis Galton and Karl Pearson pioneered the study of regression analysis and correlation analysis which has been widely used in various field of modern world. Sir Ronald A. Fisher applied statistics to diversified fields such as genetics, biometry, psychology and education, agriculture etc. So R. A. Fisher is regarded as the father of statistics. 1.2 Meaning and Definition of Statistics The word statistics have been derived from the Latin word 'status' or Italian word 'statista' or German word 'statistik' or French word 'statistique', each of which means a political state. The word 'statistics' is used in singular as well as plural sense. Thus it is usually defined in two different senses, one is singular sense and other is plural sense. In singular sense, it means the statistical methods and techniques for dealing numerical data. The acts of dealing data are collection, presentation, analysis and the interpretation of the numerical figures. On the other hand, statistics means systematic collection of quantitative information of facts (or simply data) in plural sense. i. In singular sense Statistics means the science of statistical methods embodying the theory and techniques used for collecting, analyzing and drawing inferences from the numerical data. And it is defined in singular senses as follows: "Statistics is the science of the measurement of social organism, regarded as a whole in all its manifestations". –A.L. Bowley "The science and art of handling aggregate of fats, observing, enumeration, recording, classifying and otherwise treating them". –Harlow "Statistics may be regarded as the science of collection, presentation, analysis and interpretation of numerical data". - Croxton and Cowden In singular sense, statistics means the various methods and techniques adopted for the collection, presentation, analysis and interpretation of the figures. Introduction to Statistics Unit 1
2 A Textbook of Probability and Statistics for BCA ii. In Plural Sense Statistics is defined in plural sense as follows: "Statistics are the classified facts representing the conditions of the people in a state craft. Specially those facts which can be stated in number or in tables of numbers or in any tabular or classified arrangement". –Webster "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 reasonable standard or accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other." - Prof. Horace Secrist In plural sense, statistics mean the quantitative information or numerical facts collected systematically. But, for a layman, statistics is simply a mass of figures. Hence, statistics is a science which studies the combination of the numerical data for analysis and interpretation as well as the methods and principles applied in collecting, presenting, analysis and interpreting the data under the study. 1.3 Division of Statistics Nowadays, the word statistics is used in two contexts. In one context, singular sense, it refers to a subject of study that deals with various scientific methods, which are essential from the initial stage of data collection to the final stage of data presentation. In other context, plural sense (plural of the statistics), it refers to the numerical results obtained by applying statistical methods to a set of data. All the published numerical data on business, finance, population, health, environment etc. constitute statistics in the plural sense. The subject of statistics is divided into following parts: a. Mathematical statistics. b. Applied statistics. c. Descriptive statistics. d. Inferential statistics. Mathematical statistics deals with the development of statistical theory and methods based on certain principles and mathematics, while the applied statistics deals with the applications of statistical methods to the data. In this context, business statistics is considered as applied statistics. The statistics is also divided into descriptive and inferential statistics. Descriptive statistics is used to summarize or present the data, either numerically or graphically. Numerical descriptors of data include the followings: i. One-way or two-way frequency tables. ii. Various kinds of summary measures, such as mean, variance, correlation coefficient and so on. ii. Statistical models. While graphical summarizations include various kinds of charts and graphs, such as pie chart, line graph, scatter plot and so on. The main objective of this book is to describe descriptive statistics. Inferential statistics is used to draw inferences about the population from sample data drawn from the population. These inferences may take the form of answers to yes/no questions (hypothesis testing), estimates of numerical characteristics (estimation). Inferential statistical methods involve quite advanced methods and will not be considered in this book. Learning of the statistics will require the knowledge of basic mathematics. Like in other disciplines, statistics has its own vocabularies. An important and most frequently used term in statistics is variable. Whenever such terminologies are felt necessary to use we shall explain them.
Introduction to Statistics 3 If we observe or measure a characteristic we find that it takes on different values in different persons, places, or things, and it is customary to label the characteristics a variable. Some examples of variables include salary, age, sex, post, and educational degree of employees of a company, amount of daily sales of a store and marks obtained by the students in an examination. Data are considered as the values of a variable (in case of univariate data) or values of several variables (in case of multivariate data). The values of variable are generated by measuring, asking or observing the characteristics of similar subjects under the study. Data generated by quantitative variables (such as salary, age, amount of sales, and so on) are called quantitative data, while the data generated by qualitative variables (such as sex, post, educational degree and so on) are called qualitative data or categorical data. 1.4 Functions of Statistics Statistics is applied in everywhere therefore no nation exists without numerical fact in figure. The functions of statistics are as follows: a. Statistics simplifies the complexity: The function of statistics is to present the huge mass of figures into a simple, presentable and understandable form. Using various statistical techniques, the complexity can be reduced in simplest form of the information obtained from the study. b. Statistics present the facts in a definite firm: Another important function of statistics is to present the information of facts in a quantitative form. By definition, statistics presents any kind of information under the investigation in figure and number, so the conclusion stated in numerical figure is definite. c. Statistics provides techniques of comparison: Different statistical methods and procedures facilitate comparison of the relevant features of several data. The statistical methods such as average, measure of dispersion, ratio etc. help in comparison between phenomena which enable to draw conclusion. d. Statistics helps in forecasting: In business and industry, forecasting the future based on past experience and analyzing the historical tendencies is the most important task. This can be done with the help of several statistical techniques such as regression analysis, analysis of time series, index number etc. Prediction of future trends obtained from the application of statistical techniques in an investigation related to the business and management is important and is more convincing in framing plans and policies. e. Statistics helps in formulating policies: The policy formulation of any firm, organization, business agency, bank, and nation will be suitable, if it is framed on the basis of statistical analysis and information. Making future policy is challengeable task. Statistics provides basic requirements for framing the future policies. f. Statistics gives the idea about possibilities of certain events: Probability theory is one of the major areas of statistics. We can find the occurrence and non-occurrence of events with the help of probability laws and rules. g. Statistics helps in formulating and testing hypothesis: To draw conclusion and to develop new theories in economics and business, formulation and testing the hypothesis is one of the important tasks. Formulating and testing the hypothesis without certain statistical techniques are incomplete. Testing hypothesis with the absence of statistical procedures and methods mislead the conclusion. h. Statistics helps to draw valid conclusion: It is difficult task to enumerate each and every members of population (universe) under the study of some phenomena. The statistical technique such as sampling offers the best and scientific idea to study the sample group and generalize the conclusion so obtained in
4 A Textbook of Probability and Statistics for BCA the universe. An investigator or researcher can draw inferences about the whole universe by applying the different statistical techniques. Hence statistics helps to draw valid conclusion of the study. i. Statistics provides techniques for organizing data scientifically: Collected data are in the raw form. They need to organize scientifically. Statistics provides techniques that help us to organize data scientifically. Nowadays it is customary to organize data in computer. Organization or management of the data is very essentials in modern research, since well organized data eases the work of data analysis and helps for drawing desired information very quickly. 1.5 Scope and Limitation of Statistics Statistics is not only viewed as the device for collecting data but as a mean of technique for their handling and analysis as well as drawing inferences from them. Likewise, it is not the by-product of administrative set up of the state but it embraces all kinds of sciences such as social, physical and natural. Because of its widespread uses and applications in various diversified fields such as agriculture, industry, sociology, biometry, planning, economics, business, management, psychometry, insurance, accountancy etc, it is rather impossible to think any sphere of human activity where statistics does not creep on. Such wide use of statistics in the fields of the human activity shows the scope and importance of statistics. The scopes of statistics in different disciplines are discussed as follows: i. Statistics in planning To achieve the expected goal and objective, planning is the first constraint in any fields of the universe. Especially in the field of business and management, for the efficient working and formulating policy and decisions, the planning is restored. The statistical information related to production, consumption, prices, demand, supply, investment, income, expenditure etc, as well as the advanced statistical techniques such as index number, analysis of time series and regression analysis all are used in policy formulation and future planning of business organization, industry and state also. Now-a -days, efficient planning in every field is compulsory. Thus this modern age is also known as "age of planning". ii. Statistics in economics Statistical data and advanced techniques of statistical analysis solve the varieties of economic problems such as production, consumption, distribution of income and wealth, wages, prices, profits, savings, expenditure, unemployment, investment, poverty etc. Statistical techniques have been used in determining the measure of Gross National Product and Import-Export analysis. Furthermore, the advanced statistical techniques have been successfully used in the analysis of cost functions, production functions and consumption functions. Use of statistics in economics has led to the formulation and establishing the economic theory and laws such as Engel's law of consumption, Samuelson's Revealed Preference Analysis, Use of Analysis of Time Series, Index Number and Demand Analysis in Economic Planning, Development of New Discipline; Econometrics etc. Thus, the interaction between statistics and economics is the effective use of statistics in formulation of economic theories and economic policies. In fact, statistics got so much integrated with economics that it led to the development of a new subject called econometrics which basically deals with economic issues involving use of statistics. iii. Statistics in business and management It is universally accepted that statistical data and the powerful statistical tools such as probability theory, expectation, sampling techniques, and tests of significance, estimation theory, analysis of time series, index number, forecasting techniques and so on play indispensable role in decision making. The use of statistical data and techniques is indispensable in almost all branches of business. It is difficult to have success in business if careful study of the market is not made. Statistics helps in formulating