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introduction, , Chapter |, , Introduction, , , , ——, , ae G-Pen t-te, Statistics., , oe, , , , , , , , Itis interesting to see the reputation of Statistics. Disraeli said, ‘There, are three kinds of lies, - lies, damned lies and statistics’. One of the more, amusing and informative book by Darrel Hutf is entitled: “How to Lie, with Statistics.’ Besides the errors that statisticians make, the use of, jargon makes the layman suspicious of statistics. People feel that, statistics can be used to prove any dishonest theses. By studying, statistics people can make sure that they will not be lied to by any, statistician, using statistics in an improper manner. By proper education, ignorance and error can Le reduced., , The word statistics describes several concepts of importance to, decision-maker. It is important for a beginner to have an understanding, of these different concepts., , Statistical Methods v/s Experimental Methods, , We try to get the knowledge of any phenomenon through direct, experiment. There may be many factors affecting a certain phenomenon, simultaneously. If we want to study the effect of a particular factor, we, keep other factors fixed and study the effect of only one factor. This is, Possible in all exact sciences like physics, chemistry, etc. This metho¢, cannot be used in many sciences, where all the factors cannot be isolatec, and controlled. This difficulty is particularly encountered in socia, Sciences, where we deal with human beings. No two persons are exactlh, — the environment also changes and it has its effect on ever, thes sce = a it is not possible to study one factor keepin;, obtained by . — tte we use statistical methods. The result, obtained by ex of this science will not be as accurate as thos, , Y experimental methods. Even then they are of much use an
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3 roe Vipest’s™ Business Statistics (BMS), , important role to play in the modern world. Even in, ae eis aee wr the statistical methods are made use of., The word statistics is derived from the Latin word ‘Statis’ which, , | state. The word statistics was originally applied to only, wry Sd : that were required by the state for official, , , , though the collection of data for other, To ', peg are Pera ruled out. The word has now acquired a, , wider meaning., , 1.1 Statistics in Plural, , Statistics in Plural refer to any set of data or information. The, president of a company may call for ‘statistics on the sales of northern, region’ or an MP may quote the statistics on price-rise in agricultural, products. More familiar examples for the students will be the marks of, students in a class, the ages of children in primary school., , Prof. Secrist defines the word ‘Statistics’ in the first sense as follows:, , “By Statistics we mean aggregate of facts affected to a marked exten;, by multiplicity of causes, numerically expressed, enumerated o;, estimated according to reasonable standards of accuracy, collected in a, systematic manner for a predetermined purpose and placed in relation, to each other.” ., , / This definition gives all the characteristics of Statistics:, (, , i) Aggregate of facts: A single isolated figure is not ‘Statistics.’ Marks, of one student in one subject will not be called statistics. But if we, consider the marks of all the students in the class in a particular, subject, they will be called ‘Statistics’., , fi) Affected by multiplicity of causes: There are various causes for the, changes in the data, the marks of the students depend upon, the, intelligence of students, their capacity and desire to work etc., , ii) Numerically expressed; Unless the characteristics have some, numerical measurement they will not be called statistics. The, , statement ‘A student writes very good English’ is not statistics. But, , if marks of the whole class in ‘English’ ill be called, err ! glish’ are given they will, , iv) Enumerated or Estimated according to reasonable standards of, , accuracy: However much a Person tries, it is not possible to attain, , i perfect accuracy whether we actually measure or estimate the, , | characteristic. But a certain standard of accuracy should be set up, i according to the problem under consideration. The estimate for
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Introduction ‘ ‘ ree °, , cost of a big project may be correct up to Rs. 1,000 but for, household expenses it should be correct upto a Rupee., , (v) Collected in a systematic manner: There should be a method in the, manner of collection, then only the figures will be reliable and, useful. |, , (vi) Collected for a predetermined purpose: Unless we know the, purpose, the data collected may not be sufficient. Besides some, unnecessary information may be collected which will be a waste of, time and money., , (vii) Placed in relation to each other: Only when we want to compare, characteristics, which have some relation with each other, we collect, statistics. The wages of fathers and ages of sons should not be, collected together. But we can have ages and heights of a group of, persons, so that we can find the relation between the two., , 1.2 Statistical Methods, , The word statistics used in the second sense means the set of, techniques and principles for dealing with data., , (1) Suppose you have the data about production profits and sales for, a number of years of a company. Statistics in this sense is concerned, with questions such as (i) What is the best way to present these data for, review? (ii) What processing is required to reveal more details about the, data? (iii) What ratios should be obtained and reported?, , (2) A public agency wants to estimate the number of fish in a lake., Five hundred fish are captured in a net tagged and returned to the lake., One week later 1,000 fish are captured from the same lake imnets and 40, are found to be with tags. Here Statistics in this second sens#deals with, questions such as (i) What is a good estimate of the number of fish in the, lake? (ii) What is our confidence in it and how much error can be, expected? (iii) Can we have a method, which will make a better, estimate? °, , Statisticians have defined this in various ways. Bowley says,, ‘Statistics may rightly be called the science of averages’. But this, , definition is not correct. Statistics has many refined techniques and it, does much more than just averaging the data. ', , _Kendall defines it as, ‘The branch of scientific methods that ‘deals, with the data obtained by counting or measuring the properties of, , -opulation of natural phenomena’. This definition does not give the idea, ibout the functions of statistics. It is rather vague.
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uw ae us vere VTE IS Fs ROE 2 (OMS), 4, , Seligman defines it as, ‘The science which deals with the methods of, collecting, classifying, presenting, comparing and interpreting numerical, data collected to throw some light on any sphere of inquiry. Croxton,, Cowden and Klein define it as, ‘the collection, presentation, analysis and, , interpretation of numerical data.’ The last two definitions can be, considered to be proper which explain the utility of ‘statistics’. We will, examine the four procedures mentioned in the definition in brief., Collection: The data may be collected from various published and, unpublished sources, or the investigator can collect his own information., Collecting first-hand information is a very difficult task. The usefulness, of the data collected depends to a very great extent upon the manner in, which they are collected. In the next chapter we are going to discuss the, various methods of collecting data. Though theoretical knowledge is, , necessary for the proper collection of data, much can be learnt through, experience and observation., , , , Presentation: The data collected, to be understood, should be, , presented in a suitable form. Just a given mass of figures signifies, nothing to a person and they can lead only to confusion. They are, usually presented in a tabular form and represented by diagrams., , Analysis: Presentation of data in a tabular form is one elementary, step in the analysis of the collected data. If we want to compare two, series, a typical value for each series is to be calculated. If we want to, , study some characteristic of a big group, exhaustive study is not, possible. We take a sample, study it and inferences are drawn on the, basis of sample studies. Sometimes forecasting is necessary. The, , management of a firm may be interested in future sales. For that it has to, analyse the past data. We are, , going to study some of these methods of, analysing the data in this book, , methods, which are exact. For j, dealing with some psychological, person. (An economist, though well, , not be of any use there.) versed in statistical methods will, \, , ) 4
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Introduction ae ', , 13 = Statistics as Measures, , Statistics also has a precise technical meaning. Measures derived, from the sample data are referred to as Statistics. If only one measure is, obtained it is called a Statistic., , A magazine takes a sample of 100 readers. 15 of them are over 30, years of age. The sample proportion of readers over 30 years of age is, 0.15. This sample proportion is referred to as a statistic obtained by this, survey., , The weekly sales for 5 weeks for a salesman are Rs. 2,000, Rs. 2,500,, Rs. 15,000, Rs. 3,000, Rs. 1,800. As a measure of the spread of the values, the difference between the smallest and the largest value (called the, range) is calculated. This range is a statistic., , 1.4 Importance of Statistics, , Statistics is not studied for its own sake. It is employed as a tool to, study the problems in various natural and social sciences. The analysis, of data is used ultimately for forecasting, controlling and exploring., , Statistics is important because it makes the data comprehensible., Without its use the information collected will hardly be useful. To, understand the economic condition of any country we must have, different economic aspects quantitatively expressed and’ properly, presented. If we want to compare any two countries, statistics is to be, used. For studying relationship between two phenomena, we have to, take the help of statistics, which explains the correlation between the, two., , People in business can study past data and forecast the condition of, their business, so that they can be ready to handle the situations in, future. Nowadays a businessman has to deal with thousands of, employees under him and cannot have direct control over them., Therefore, he can judge them all and control their performance using, statistical methods e.g., he can set up certain standards and see whether, the final product conforms to them. He can find out the average, production per worker and see whether any one is giving less, i.e., he is, not working properly., , Business must be planned properly and the — to be fruitful, must be based on the right analysis of complex statistical data. A banker, has to study the pattern in the demand for money by his clients, so that, he will have correct amount of reserves ready. », , Scientific research also uses statistical methods, Whil exploring new, theories, the validity of the theory is to be tested only by basing statistical, methods. Even in business many new methods are introduced. Whether
