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UNIT – 1
BUSINESS STATISTICS
What is Statistics?
The word “Statistics” has been derive from the Latin word “Status” or Italian word “Statista” or German word “Statistika”. Each of these words means Political State. Initially, Statistics was used to collect the information of the people of the state about their income, health, illiteracy and wealth etc.
But now a day, Statistics has become an important subject having useful application in various fields in day to day life.
Statistics in Plural Sense:--
In the plural sense, Statistics refers to information in terms of numbers or numerical data such as Population Statistics, Employment Statistics etc. However any numerical information is not statistics.
Example: Ram gets ൟ100 per month as pocket allowance is not Statistics. It is neither an aggregate nor an average. Whereas average pocket allowance of the students of Class X is ൟ per month and there are 80 students in class XI & 8 students in Class XII are Statistics.
The following table shows a set of data that which is Statistics and which is not Statistics.
Data which are not Statistics Data which are Statistics A cow has 4 legs. Average height of the 26 plus male people in India is 6 feet compare to 5 feet in Nepal. Ram has 200 rupees in his pocket. Birth rate in India is 18 per thousand compare to 8 per thousand in USA. A young lady was run over by a speeding truck at 100 km per hour.
Over the past 10 years, India has won 60 test matches in cricket and lost 50.
From above information we can say that “All Statistics are data, but all data are not Statistics”
Definition:-
According to Bowley - “Statistics are numerical statements of facts in any department of enquiry placed in relation to each other.”
According to Yule and Kendall ----- “By Statistics we mean quantitative data affected to marked extent by multiplicity of causes.”
Characteristics of Statistics in Plural Sense
Main characteristics of Statistics in terms of numerical data are as follows:
(1) Aggregate of Facts – A single number does not constitute Statistics. We can not draw any conclusion from single number. We can draw any conclusion by the aggregate number of facts. For example, if it is stated that there are 1,000 students in our college then it has no significance. But if it is stated that there are 300 students in arts, 400 students in commerce and 300 in science in our college. It makes statistical sense as this data convey statistical information. Similarly if it is stated that population of India is 130 crore or the value of total exports from India is ൟ11, 66,439 crore then these aggregate of facts will be termed as Statistics. (2) Numerically Expressed - Statistics are expressed in terms of numbers. Qualitative aspects like small or big, rich or poor etc. are not statistics. For instance if we say that Irfan Pathan is tall Sachin is short then this statement has no statistical sense. However if it is stated that height of Irfan Pathan is 6 ft and 2 inch and the height of Sachin is 5 ft and 4 inch then these numerical will be called Statistics. (3) Affected by Multiplicity of Causes – Statistics are not affected by any single factor but it is affected by many factors. For instance 30% rise in prices may have been due to several causes like reduction in supply, increase in demand, shortage of power, rise in wages, rise in taxes, etc. (4) Reasonable Accuracy - A reasonable degree of accuracy must be kept in view while collecting statistical data. This accuracy depends on the purpose of investigation, its nature, size and available resources. (5) Pre-determined Purpose - Statistics are collected with some pre-determined objective. Any information collected without any definite purpose will only be a numerical value and not Statistics. If data pertaining to the farmers of a village is collected, there must be some pre-determined objective. Whether the statistics are collected for the purpose of knowing their economic position or distribution of land among them or their total population. All these objectives must be pre – determined. (6) Collected in a Systematic Manner – Statistics should be collected in a systematic manner. Before collecting the data, a plan must be prepared. No conclusion can be drawn from data collected in haphazard manner. For instance, data regarding the marks secured by the students of a college without any reference to the class, subject, examination, or maximum marks, etc will lead no conclusion.
number of elements is not limited then the population is infinite. Mostly we deal with finite population.
- Sample: It is a part of the population selected by some sampling procedure. The process of selection of sample is known as sampling. The number of objects in the sample is called the size of the sample. It is believed that a sample is best representative of the population.
For instance, suppose a research worker is required to study the weight of fishes in a pond after a particular period of growth. For this purpose suppose that there are 3, fishes in the pond, he may either measure the weight of all the fishes in the pond or he may decide to select a small group of fishes and measure their weights. The first approach of measuring the weight of all fishes is called complete enumeration or census. Another approach in which only a small group of fishes is considered is called sample survey. In brief we can say that in complete enumeration, information is collected on all the units of the universe and in sample survey, only a part of the universe is considered.
3. Variable: A property of objects is known as variable which differ from object to object and is expressible numerically, in terms of numbers. For instance: the marks in Mathematics of students in a class can be expressed in the term of marks obtained by the students. So it is a variable property which is expressible quantitatively.
- Attribute: A property and characteristic of objects is known as attribute which are not expressible quantatively in number. We can express the data qualitatively. For example, smoking, color, honesty etc.
CHARACTERISTICS OF STATISTICS
1. Statistics are aggregate of facts. 2. Statistics are numerically expressed. 3. Statistics are affected to a marked extent by multiplicity of causes. 4. Statistics are either enumerated or estimated with reasonable standard of accuracy 5. Statistics are collected in a systematic manner. 6. Statistics are collected for a pre-determined purpose. 7. Statistics should be placed in relation to each other.
In the absence of the above characteristics numerical data can’t be called Statistics and hence “all statistics are numerical statements of facts but all numerical statements of facts are not statistics. ”
According to above Definitions , Statistics is both a science and an art. It is related to the study and application of the principles and methods applicable in the collection ,
presentation , analysis, interpretation and forecasting of data. Or statistical facts influenced by several factors and related to any area of knowledge or research so that concrete and intelligent decisions may be taken in the phase of uncertainty
NATURE OF STATISTICS
Statistics as a science: science refers to a systematized body of knowledge. It studies cause and effect relationship and attempts to make generalizations in the form of scientific principles or laws. “Science, in short, is like a light house that gives light to the ships to find out their own way but doesn’t indicate the direction in which they should go.” Like other sciences, Statistical Methods are also used to answer the questions like, how an investigation should be conducted. In what way the valid and reliable conclusions can be drawn? Statistics is called the science of scientific methods.
In words of Croxton and Cowden , “ Statistics is not a science, it is scientific methods. ” According to Tippet , “ as science, the statistical method is a part of the general scientific method and is based on the same fundamental ideas and processes. ”
Statistics as an art: we know that science is a body of systematized knowledge. How this knowledge is to be used for solving a problem is work of an art. An art is an applied knowledge. It refers the skill of handling facts so as to achieve a given objective. It is concerned with ways and means of presenting and handling data, making inferences logically and drawing relevant conclusion. Art aspects of statistics tell, ‘how to use statistical rules and principles to study the problems and finding their solutions. ‘Collections of statistics (data) its use and utility are itself an art.
Statistics is both science and art: After studying science and art aspects of statistics, it is used not only to gain knowledge but also to understand the facts and draw important conclusions from it. If science is knowledge, then art is action. Looking from this angle statistics may also be regarded as an art. It involves the application of given methods to obtain facts, derive results and finally to use them for devising action.
STAGES IN A STATISTICAL INVESTIGATION 5 stages -
1. Collection: This is the primary step in a statistical study and data should be collected with care by the investigator. If data are faulty, the conclusions drawn can never be reliable. The data may be available from existing published or unpublished sources or
Collection Organisation Presentation
Analysis Interpretation
1. Statistics and the State: in recent years the functions of the state have increased tremendously. The concept of the state has changed from that of simply maintaining law and order to that of a welfare state. Statistical data and statistical methods are of great help in promoting human welfare. The government in most countries is the biggest collector and user of statistical data. These statistics help in framing suitable policies. 2. Statistics in Business and Management: with growing size and increasing competition, the problems of business enterprises have become complex. Statistics is now considered as an indispensable tool in the analysis of activities in the field of business, commerce and industry. The object can be achieved by properly conducted market survey and research which greatly depends on statistical methods. The trends in sales and production can be determined by statistical methods like time-series analysis which are essential for future planning of the phenomena. Statistical concepts and methods are also used in controlling the quality of products to satisfaction of consumer and the producer. The bankers use the objective analysis furnished by statistics and then temper their decisions on the basis of qualitative information. 3. Statistics and Economics: R.A.Fisher complained of “the painful misapprehension that statistics is a branch of economics.” Statistical Data and methods are of immense help in the proper understanding of the economic problems and in the information of economic policies. In the field of exchange, we study markets, law of prices based on supply and demand, cost of production, banking and credit instruments etc. The development of various economic theories own greatly to statistical methods, e.g., ‘Engel’s law of family expenditure’, ‘Malthusian theory of population’. The impact of mathematics and statistics has led to the development of new disciplines like ‘Econometrics’’ and ‘Economic Statistics’. In fact, the concept of planning so vital for growth of nations would not have been possible in the absence of data and proper statistical analysis. 4. Statistics and Psychology and Education: Statistics has found wide application in psychology and education. Statistical methods are used to measure human ability such as; intelligence, aptitude, personality, interest etc. by tests. Theory of learning is also based on Statistical Principles. Applications of statistics in psychology and education have led to the development of new discipline called ‘Psychometric’. 5. Statistics and Natural science; Statistical techniques have proved to be extremely useful in the study of all natural sciences like biology, medicine, meteorology, botany etc. for example- in diagnosing the correct disease the doctor has to rely heavily on factual data like temperature of the body, pulse rate, B.P. etc. In botany- the study of plant life, one has to rely heavily on statistics in conducting experiments about the plants, effect of temperature, type of soil etc. In agriculture- statistical techniques like ‘analysis of variance’ and ‘design of experiments’ are useful for isolating the role of manure, rainfall, watering process, seed quality etc. In fact it is difficult to find any scientific activity where statistical data and methods are not used.
6. Statistics and Physical Science: The physical sciences in which statistical methods were first developed and applied. It seems to be making increasing use of statistics, especially in astronomy, chemistry, engineering, geology, meteorology and certain branches of physics. 7. Statistics and Research; statistics is indispensable in research work. Most of the advancement in knowledge has taken place because of experiments conducted with the help of statistical methods. Statistical methods also affect research in medicine and public health. In fact, there is hardly any research work today that one can find complete without statistical methods. 8. Statistics and Computer: The development of statistics has been closely related to the evolution of electronic computing machinery. Statistics is a form of data processing a way of converting data into information useful for decision-making. The computers can process large amounts of data quickly and accurately. This is a great benefit to business and other organizations that must maintain records of their operations. Processing of row data is extensively required in the application of many statistical techniques.
CLASSIFICATION OF STATISTICS
Statistics can be divided into 3 parts;
1. Descriptive Statistics: Descriptive statistics is related to numerical data or facts. Such data are collected either by counting or by some other process of measurement. It is also related to those methods, includes editing of data, classification, tabulation, diagrammatic or graphical presentation, measures of central tendency, measures of dispersion, correlation etc., help to make the description of numerical facts simple, systematic, synoptic understandable and meaningful. 2. Inferential Statistics: Inferential statistics help in making generalizations about the population or universe on the basis of study of samples. It includes the process of drawing proper and rational conclusion about the universe. Among these methods, probability theory and different techniques of sampling test are important. 3. Applied Statistics; It involves application of statistical methods and techniques to the problems and actual facts. For example-statistics related to national income, industrial and agricultural production, population, price etc. are called applied statistics. It can be divided into 2 parts-(1) Descriptive Applied Statistics- it deals with the study of the dat
DESCRIPTIVE STATISTICS
INFERENTIAL STATISTICS
APPLIED STATISTICS
about what to produce, how much to produce, when to produce is based on facts analyzed statistically.
(C) Distribution- Statistics play a vital role in the field of distribution. We calculate the national income of a country by statistical methods and compare it with other countries. At every step we require the help of figures without them. It is difficult to move and draw inferences.
4. Importance in Planning; for the proper utilization of natural and manual resources, statistics play a vital role. Planning is indispensable for achieving faster rate of growth through the best use of a nation’s resources. Sometimes said that, “Planning without statistics is a ship without rudder and compass.” For example- In India, a number of organizations like national sample survey organization(N.S.S.O.), central statistical organization (C.S.O.) are established to provide all types of information. 5. Importance in Business: The use of statistical methods in the solution of business problems dates almost exclusively to the 20th^ century. Or now days no business, large or small, public or private, can prosper without the help of statistics. Statistics provides necessary techniques to a businessman for the formulation of various policies and planning with regard to his business. Such as- (A) Marketing- In the field of marketing, it is necessary first to find out what can be sold and them to evolve a suitable strategy so that goods reach the ultimate consumer. A skillful analysis of data on population, purchasing power, habits of people, competition, transportation cost etc. should precede any attempt to establish a new market. (B) Quality Control- To earn the better price in a competitive market, it is necessary to watch the quality of the product. Statistical techniques can also be used to control the quality of the product manufactured by a firm. Such as - Showing the control chart. (C) Banking and Insurance Companies- banks use statistical techniques to take decisions regarding the average amount of cash needed each day to meet the requirements of day to day transactions. Various policies of investment and sanction of loans are also based on the analysis provided by statistics. (D) Accounts writing and Auditing - Every business firm keeps accounts of its revenue and expenditure. Statistical methods are also employed in accounting. In particular, the auditing function makes frequent application of statistical sampling and estimation procedures and the cost account uses regression analysis. (E) Research and Development- Many business organizations have their own research and development department which are responsible for collection of such data. These departments also prepare charts groups and other statistical analysis for the purpose.
FUNCTIONS OF STATISTICS
Statistics performs the functions of making the numerical aspects of facts simple, precise, comparable and reliable. In fact, the various functions performed by statistics are the basis of its
utility. R.W. Burgess says, “The fundamental gospel of statistics is to push back the domain of ignorance, prejudice, rule of thumb, arbitrary and premature decisions, tradition & dogmatism and to increase the domain in which decisions are made. Principles are formulated on the basis of analyzed quantitative facts.”
1. Numerical and definite expression of facts: The first function of the statistics is the collection and presentation of facts in numerical form. We know that the numerical presentation helps in having a better understanding of the nature of a problem. One of the most important functions of statistics is to present general statements in a precise and definite form. Statements and facts conveyed in exact quantitative terms are always more convincing than vague utterances. 2. Simplifies the data (condensation): Not only does statistics present facts in a definite form but it also helps in condensing mass of data into a few significant figures. According to A.E.Waugh, “ the purpose of a statistical method is to simplify great bodies of numerical data. ” In fact, human mind cannot follow the huge, complex and scattered numerical facts. So these facts are made simple and precise with the help of various statistical methods like averages, dispersion, graphic or diagrammatic, presentation, classification, tabulation etc. so that a common man also understand them easily. 3. Comparison of facts: Baddington states , “The essence of the statistics is not only counting but also comparison.” The function of comparison does help in showing the relative importance of data. For example- the pass % of examination result of a college may be appreciated better when it is compared with the result of other college or the results of previous years of the same college. 4. Establishment of relationship b/w two or more phenomena; to investigate the relationship b/w two or more facts is the main function of statistics. For example-demand and supply of a certain commodity, prices and wages, temperature and germination time of seeds are interrelated. 5. Enlarges individual experiences: In word of Bowley, “the proper function of statistics indeed is to enlarge individual experience.” Statistics is like a master key that is used to solve problems of mankind in every field. It would not be exaggeration to say that many fields of knowledge would have remained closed to the mankind forever but for the efficient and useful techniques and methodology of the science of statistics. 6. Helps in the formulation of policies: statistics helps in formulating policies in different fields, especially in economic, social and political fields. The government policies like industrial policy, export-import policies, taxation policy and monetary policy are determined on the basis of statistical data and their movements, plan targets are also fixed with the help of data. 7. Helps in forecasting: statistical methods provide helpful means in estimating the available facts and forecasting for future. Here Bowley’s statement is relevant that, “a statistical estimate may be good or bad, accurate or the reverse; but in almost all cases it is likely to be more accurate than a casual observer’s impression.”
6. Statistics is only one of the methods of studying a phenomenon; According to Croxton & Cowden, “It must not be assumed that the statistical method is the only method to be used in research; neither this method be considered the best attack for every problem.” The conclusions arrived at with the help of statistics must be supplemented with other evidences. 7. Statistical results may be misleading; Without any reference, statistical results may provide doubtful conclusions. For example – on the basis of increasing no. of prisoners in the prison, it may be conclude that crime is increasing. But it may be possible that due to rude behavior of police administration the number of prisoners is increasing but crime is decreasing.
Therefore, it is worth-mentioning that every science based on certain assumption and limitations. This does not reduce the importance of the subject but lays emphasis on the fact that precautions should be taken while dealing with statistical analysis and interpretations.
DISTRUST OF STATISTICS
For practical view point statistics is very useful and important science. We know that utility of statistics lies not merely in data but in correct analysis and proper interpretation of data. Several times due to ignorance and bias, people misuse this delicate tool of knowledge and it creates distrust about data.
Opinion about distrust of statistics ;
1 stOpinion – Statisticians fully trust on the statistical conclusions because data is collected, edited, analyzed and interpreted on the basis of statistical methods. Thus there is no reason to doubt on it and said that “Figures don’t lie” or “Figures can prove nothing.”
2 nd^ Opinion – The statistics is looked upon with a suspicious eye and is quite often condemned as “Figures are tissue of flesh hood. Discardi remarks that there are three kinds of lies- lies, damned lies and statistics or “There are black lies, white lies, multi-chromatic lies and statistics is rainbow of lies.”
Many persons feel that data are false, confusing and incorrect and with their help truth can be proved wrong and lies can be put as truth. Hence it is said that “Statistics can prove anything” or “Statistics are like clay of which you can make God or Devil, as you please.”
In this context, the observation is worth quoting that “Statistician is the person who is deeply involved in statistical data. He can freely play with them, misuse them and can cheat common people. So he is just magician who shows the games of tricks of hand through statistical data. His result can be surprising but not trustworthy.
TYPES OF DATA
Data are the foundation stones and basic raw material in relation to any statistical investigation that can be counted, classified, measured or quantified.
Types of Data are following;
ON THE BASIS OF CHARACTERISTICS OF FACTS
Data may be divided into two types;
1. Quantitative Data or Numerical Data: These types of data can be measured directly such as age, income, production, marks etc. those facts are called variables and variables may be discrete or continuous. Discrete variable– Those variables whose values are individually distinct and discontinuous. There is a definite difference between two variables. According to Boddington, “Discrete variables is one where the variables (Individual values) differ from each other by definite
Terms like ‘Data Point’ and ‘Data Set’ are also used in order to distinguish between the numbers relating to individual or single facts and the aggregate of facts. For example– the data of production of sugar for ten years will be termed as ‘Data Set’ and the figures for production of one year will be as ‘Data Point’.
CLASSIFICATION
After collection and editing of data the first step towards further processing the same is classification. Classification is a process in which the collected data are arranged in separate classes, groups or subgroups according to their characteristics. According to Secrist, “Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different classes.”
It concludes that classification means the arrangements and systematization of data into different classes and these classes are determined on the basis of nature, objectives and scope of the enquiry.
OBJECTIVES OF CLASSIFICATION Classification is a method or technique for extracting the essential information supplied by the raw data.
(1) To condense the data: the main objective of classification is to condense and simplify the
statistical material, so that the same may be easily understandable.
(2) To bring out points of similarities and dissimilarities of data: classification brings out
clearly the points of similarity and dissimilarities of statistical facts because data of similar characteristics are placed in one class i.e., males and females, literates and illiterates, married and unmarried etc.
(3) To make facts comparable: by arranging the data according to the points of similarity and
dissimilarities, it helps in comparison.
(4) To bring out relationship: classification helps in finding cause and effect relationship in the
data. For example- based on literacy and criminal tendency of a group peoples, it can be established whether literacy has any impact on criminal tendency or not.
(5) To prepare ground for tabulation: tabulation is the basis of statistical analysis and
classification is the basis for tabulation.
It concludes that classification occupies an important place in the process of statistical investigation. The fact is that the process of tabulation, presentation and analysis can’t even be shorted without classification.
CHARACTERISTICS OR RULES FOR A GOOD CLASSIFICATION
(1) Unambiguity: the various classes should be so defined that there is no roomfor doubt and confusion. For example–population is classified as literates or illiterates. (2) Exhaustive and mutually exclusive: classification should be so exhaustive (clear all aspects) and one item may not be find place in more than one class. For example – students of a
college are classified into three groups – urban, rural and hostlers. This classification is not mutually exclusive because among hostlers some may be urban and some other rural. (3) Stability: the classification of data into various classes must be stable over be a period of time of investigation. (4) Suitability: the classification should confirm to the objectives of enquiry. For example–to study the relationship between sex and university education, there is no need to classify on the basis of age and religion. (5) Flexibility: a good classification should be flexible so that adjustments may be easily be made in classes according to changed situations. An ideal classification is one that can adjust itself to these changes and yet retains its stability.
METHODS OF CLASSIFICATION
There are 4 methods of classification;
TABULATION
Tabulation is the next step of classification of the data and is designed to summaries lots of information in a simple manner. In common language tabulation is the process of arranging data in a systematic manner in the form of rows and columns. According to Blair , “Tabulation in its broadest sense is any orderly arrangement of data in columns and rows.”
Geographical Classification
Chronological Classification
Qualitative Classification
Quantitative Classification
No. of children
Tally Bars Frequency
1 |||| 5 2 |||| | 6 3 |||| 4 4 ||| 3 5 || 2
(2) Continuous frequency distribution: A continuous frequency distribution is such a distribution in which data are arranged in classes or groups which are not exactly measureable. Groups or class-intervals are always in a continuous form from the beginning of the frequency distribution, till the end, within a given range of the data. For example– 39,25,5,33,19,21,12,48,13,21,9,1,10, 9,8,12,17,40,12,46,37,17,27,30,6,2,
Construction of continuous frequency distribution
(1) Find out the range = maximum marks – minimum marks
(2) Class size = decide the class size
(3) Width of class interval = ܍ܢܑܛ ܛܛ܉ܔ܋܍ܖ܉ܚ
(4) Mid value = ܜܑܕܑܔ ܛܛ܉ܔ܋ ܚ܍ܟܗܔାܜܑܕܑܔ ܛܛ܉ܔ܋ ܚ܍ܘܘܝ
(5) Class frequency = the no. of observations corresponding to a particular class is known
as frequency of the class.
Marks Tally Bars No. of Students 0 – 10 |||||| 7 10 – 20 |||| ||| 8 20 – 30 |||| 5 30 – 40 |||| 4 40 – 50 ||| 3
There are two types of series according to class interval;
(1) Inclusive form; A frequency distribution in which each upper limit of each class is also included. Such as; 0-9, 10-19, 20-29…………….. (2) Exclusive form; In which the upper limit of the next class-interval. Such as; 0-10, 10-20, 20-30…………
