Statistics for Management.pptx

Statistics for Management

1. Statistical Thinking In the context of today’s competitive business environment where many organizations find themselves data-rich but information-poor. For decision makers, it is important to develop the ability to extract meaningful information from raw data to make better decisions.  It is possible only through the careful analysis of data guided by statistical thinking

2. The views commonly held about statistics are numerous, but often incomplete. It has different meanings to different people depending largely on its use. For example, ( i ) for a cricket fan, statistics refers to numerical information or data relating to the runs scored by a cricketer; (ii) for an environmentalist, statistics refers to information on the quantity of pollutants released into the atmosphere by all types of vehicles in different cities; (iii) for the census department, statistics consists of information about the birth rate and the sex ratio in different states; iv) for a share broker, statistics is the information on changes in share prices over a period of time; and so on . Growth and development of statistics

3. The average person perceives statistics as a column of figures, various types of graphs, tables and charts showing the increase and/or decrease in per capita income, wholesale price index, industrial production, exports, imports, crime rate and so on. The sources of such statistics for a common man are newspapers, magazines/journals, reports/bulletins, radio, and television. In all such cases, the relevant data are collected; numbers manipulated and information presented with the help of figures, charts, diagrams, and pictograms; Efforts to understand and find a solution (with certain degree of precision) to problems pertaining to social, political, economic, and cultural activities, seem to be unending. All such efforts are guided by the use of methods drawn from the field of statistics Growth and development…..

4. As statistical data , the word statistics refers to a special discipline or a collection of procedures and principles useful as an aid in gathering and analysing numerical information for the purpose of drawing conclusions and making decisions. Since any numerical figure, or figures, cannot be called statistics owing to many considerations which decide its use, statistical data or mere data is a more appropriate expression to indicate numerical facts. A definition which describe the characteristics of statistics are : the classified facts respecting 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. Statistics defined

5. As statistical methods , adopted as aids in the collection and analysis of numerical information or statistical data for the purpose of drawing conclusions and making decisions are called statistical methods . Statistical methods, are also called statistical techniques, are sometimes loosely referred to cover ‘statistics’ as a subject in whole. There are two branches of statistics: ( i ) mathematical statistics and (ii) applied statistics. Mathematical statistics is a branch of mathematics and is theoretical. It deals with the basic theory about how a particular statistical method is developed. Applied statistics, on the other hand, uses statistical theory in formulating and solving problems in other subject areas such as economics, sociology, medicine, business/industry, education, and psychology Statistics defined

6. Statistical methods, broadly, fall into the following two categories: ( i ) Descriptive statistics (ii) Inferential statistics DESCRIPTIVE STATISTICS : It includes statistical methods involving the collection, presentation, and characterization of a set of data in order to describe the various features of that set of data. In general, methods of descriptive statistics include graphic methods and numeric measures. Bar charts, line graphs, and pie charts comprise the graphic methods, whereas numeric measures include measures of central tendency, dispersion, skewness, and kurtosis Types of statistical methods

7. INFERENTIAL STATISTICS : It includes statistical methods which facilitate estimating the characteristics of a population or making decisions concerning a population on the basis of sample results. Sample and population are two relative terms. The larger group of units about which inferences are to be made is called the population or universe, while a sample is a fraction, subset, or portion of that universe . The need for sampling arises because in many situations data are sought for a large group of elements such as individuals, companies, voters, households, products, customers, and so on to make inferences about the population that the sample represents. Types…

8. Thus, due to time, cost, and other considerations data are collected from only a small portion of the population called sample. The concepts derived from probability theory help to ascertain the likelihood that the analysis of the characteristics based on a sample do reflect the characteristics of the population from which the sample is drawn. This helps the decision-maker to draw conclusions about the characteristics of a large population under study Types…

9. The scope of application of statistics has assumed unprecedented dimensions these days. Statistical methods are applicable in diverse fields such as economics, trade, industry , commerce, agriculture, bio-sciences, physical sciences, education, astronomy, insurance , accountancy and auditing , sociology , psychology and so on. United states commissioner has explained the importance of statistics by saying: to a very striking degree our culture has become a statistical culture. Even a person who may never have heard of an index number is affected by those index numbers which describe the cost of living. It is impossible to understand psychology, sociology, economics or a physical science without some general idea of the meaning of an average, of variation, of concomitance of sampling, of how to interprets charts and tables . IMPORTANCE AND SCOPE

10. A state in the modern setup collects the largest amount of statistics for various purposes. It collects data relating to prices, production, consumption, income and expenditure, investments, and profits . Popular statistical methods such as time-series analysis, index numbers, forecasting, and demand analysis are extensively practiced in formulating economic policies. Governments also collect data on population dynamics in order to initiate and implement various welfare policies and programmes . In addition to statistical bureaus in all ministries and government departments in the central and state governments, other important agencies in the field are the central statistical organisation (CSO), national sample survey organization (NSSO), and the registrar general of India (RGI) STATISTICS AND STATE

11. Statistical methods are extensively used in all branches of economics. For example: Time-series analysis is used for studying the behavior of prices, production and consumption of commodities, money in circulation, and bank deposits and clearings. Index numbers are useful in economic planning as they indicate the changes over a specified period of time in prices of commodities, imports and exports, industrial/agricultural production, cost of living, and the like. Demand analysis is used to study the relationship between the price of a commodity and its output (supply). Forecasting techniques are used for curve fitting by the principle of least squares and exponential smoothing to predict inflation rate, unemployment rate, or manufacturing capacity utilization STATISTICS AND ECONOMICS

12. According to Wallis and Roberts, ‘Statistics may be regarded as a body of methods for making wise decisions in the face of uncertainty.’ Ya -Lin-Chou gave a modified definition over this, saying that ‘statistics is a method of decision-making in the face of uncertainty on the basis of numerical data and calculated risks.’ These definitions reflect the applications of Statistics in the development of general principles for dealing with uncertainty . Statistical reports provide a summary of business activities which improves the capability of making more effective decisions regarding future activities. Discussed below are certain activities of a typical organization where statistics plays an important role in their efficient execution. STATISTICS IN BUSINESS MANAGEMENT

13. MARKETING before a product is launched, the market research team of an organization, through a pilot survey, makes use of various techniques of statistics to analyse data on population, purchasing power, habits of the consumers, competitors, pricing, and a hoard of other aspects. Such studies reveal the possible market potential for the product. Analysis of sales volume in relation to the purchasing power and concentration of population is helpful in establishing sales territories, routing of salesman, and advertising strategies to improve sales. Production : Statistical methods are used to carry out R&D programmes for improvement in the quality of the existing products and setting quality control standards for new ones. Decisions about the quantity and time of either self-manufacturing or buying from outside are based on statistically analysed data . Activities of typical organisation

14. Finance : A statistical study through correlation analysis of profits and dividends helps to predict and decide probable dividends for future years. Statistics applied to analysis of data on assets and liabilities , income and expenditure helps to ascertain the financial results of various operations. Financial forecasts, break-even analysis, investment decisions under uncertainty—all involve the application of relevant statistical methods for analysis. Personnel : (People work for organization) : In the process of manpower planning, a personnel department makes statistical studies of wage rates, incentive plans, cost of living, labor turnover rates, employment trends, accident rates, performance appraisal, and training and development programs. Employer-employee relationships are studied by statistically analysing various factors—wages, grievances handling, welfare, delegation of authority, education and housing facilities, and training and development Activities…

15. Currently there is an increasing use of statistical methods in physical sciences such as astronomy, engineering, geology, meteorology, and certain branches of physics. Statistical methods such as sampling, estimation, and design of experiments are very effective in the analysis of quantitative expressions in all fields of most physical sciences . Some specific areas of applications of statistics in social sciences are : Correlation & Regression analysis techniques are used to study and isolate all those factors associated with each social phenomenon which bring out the changes in data with respect to time, place, and object. Sampling techniques and estimation theory are indispensable methods for conducting any social survey. In sociology, statistical methods are used to study mortality (death) rates, fertility (birth rates) trends, population growth, and other aspects of vital statistics . Statistics in physical & Social science

16. The knowledge of statistical techniques in all natural sciences—zoology, botany, meteorology, and medicine—is of great importance. For example, for a proper diagnosis of a disease, the doctor needs and relies heavily on factual data relating to pulse rate, body temperature, blood pressure, heart beats, and body weight. An important application of statistics lies in using the test of significance for testing the efficacy of a particular drug or injection meant to cure a specific disease. Comparative studies for effectiveness of a particular drug/injection manufactured by different companies can also be made by using statistical techniques such as the t-test and f-test. To study plant life, a botanist has to rely on data about the effect of temperature, type of environment, and rainfall, and so on. Statistics in medical science

17. Computers and information technology, in general, have had a fundamental effect on most business and service organizations. Over the last decade or so, however, the advent of the personal computer (PC) has revolutionized both the areas to which statistical techniques are applied. PC facilities such as spreadsheets or common statistical packages have now made such analysis readily available to any business decision-maker. Computers help in processing and maintaining past records of operations involving payroll calculations, inventory management, railway/airline reservations, and the like. Use of computer software's, however, presupposes that the user is able to interpret the computer outputs that are generated Statistics and computers

18. Although statistics has its applications in almost all sciences—social, physical, and natural—it has its own well, which restrict its scope and utility. STATISTICS DOES NOT STUDY QUALITATIVE PHENOMEANA Since statistics deals with numerical data, it cannot be applied in studying those problems which can be stated and expressed quantitatively. For example, a statement like ‘export volume of India has increased considerably during the last few years’ cannot be analysed statistically. Also, qualitative characteristics such as honesty, poverty, welfare, beauty, or health, cannot directly be measured quantitatively. However, these subjective concepts can be related in an indirect manner to numerical data after assigning particular scores or quantitative standards. For example, attributes of intelligence in a class of students can be studied on the basis of their intelligence quotients (IQ) which is considered as a quantitative measure of the intelligence Limitations of statistics

19. By statistics we mean aggregate of facts affected to a marked extent by multiplicity of factors . . . and placed in relation to each other.’ This statement implies that a single or isolated figure cannot be considered as statistics, unless it is part of the aggregate of facts relating to any particular field of enquiry. For example, price of a single commodity or increase or decrease in the share price of a particular company does not constitute statistics. However, the aggregate of figures representing prices, production, sales volume, and profits over a period of time or for different places do constitute statistics. Statistics Does Not Study Individuals

20. The variables or numbers are defined and categorized using different scales of measurements. Each level of measurement scale has specific properties that determine the various use of statistical analysis . Using levels of measurement is another way of classifying data. Levels of Measurements There are four different scales of measurement. The data can be defined as being one of the four scales. The four types of scales are: Nominal scale Ordinal scale Interval scale Ratio scale Scale of measurements

21. Nominal and ordinal scales data from a categorical variable are measured on a nominal scale or on an ordinal scale. A nominal scale (see figure 1.3) classifies data into distinct categories in which no ranking is implied. In the good tunes customer satisfaction survey, the answer to the question are you likely to buy additional merchandise from good tunes in the next 12 months? Is an example of a nominal scaled variable, as are your favorite soft drink, your political party affiliation, and your gender. Nominal scaling is the weakest form of measurement because you cannot specify any ranking across the various categories. Figure 1.3 examples of nominal scales categorical variable categories personal computer ownership type of stocks owned internet provider growth value microsoft network other AOL other none yes no Types of scales

22. AN EXAMPLE OF A NOMINAL SCALE MEASUREMENT IS GIVEN BELOW: WHAT IS YOUR GENDER? M- MALE F- FEMALE HERE, THE VARIABLES ARE USED AS TAGS, AND THE ANSWER TO THIS QUESTION SHOULD BE EITHER M OR F. Ordinal Scale: The ordinal scale is the 2 nd  level of measurement that reports the ordering and ranking of data without establishing the degree of variation between them. Ordinal represents the “order.” Ordinal data is known as qualitative data or categorical data. It can be grouped, named and also ranked .

23. The ordinal scale shows the relative ranking of the variables It identifies and describes the magnitude of a variable Along with the information provided by the nominal scale, ordinal scales give the rankings of those variables The interval properties are not known The surveyors can quickly analyse the degree of agreement concerning the identified order of variables Characteristics of ordinary scale

24. Example: Ranking of school students – 1st, 2nd, 3rd, etc. Ratings in restaurants Evaluating the frequency of occurrences Very often Often Not often Not at all Assessing the degree of agreement Totally agree Agree Neutral Disagree Totally disagree

25. Interval Scale The interval scale is the 3 rd  level of measurement scale. It is defined as a quantitative measurement scale in which the difference between the two variables is meaningful. In other words, the variables are measured in an exact manner, not as in a relative way in which the presence of zero is arbitrary . Example: Likert scale Net promoter score (NPS) Bipolar matrix table Types…

26. Ratio Scale The ratio scale is the 4 th  level of measurement scale, which is quantitative. It is a type of variable measurement scale. It allows researchers to compare the differences or intervals. The ratio scale has a unique feature. It possesses the character of the origin or zero points. Characteristics of Ratio Scale: Ratio scale has a feature of absolute zero It doesn’t have negative numbers, because of its zero-point feature It affords unique opportunities for statistical analysis. The variables can be orderly added, subtracted, multiplied, divided. Mean, median, and mode can be calculated using the ratio scale. Ratio scale has unique and useful properties. One such feature is that it allows unit conversions like kilogram – calories, gram – calories, etc. TYPES…

27. An example of a ratio scale is: What is your weight in kgs? Less than 55 kgs 55 – 75 kgs 76 – 85 kgs 86 – 95 kgs More than 95 kgs Example:

28. There are a variety of diagrams used to represent statistical data. Different types of diagrams, used to describe sets of data, are divided into the following categories: • dimensional diagrams ( i ) one dimensional diagrams such as histograms, frequency polygones , and pie charts. (Ii) two-dimensional diagrams such as rectangles, squares, or circles. (Iii) three dimensional diagrams such as cylinders and cubes. • Pictograms or ideographs • cartographs or statistical maps Graphical descriptive techniques

29. These diagrams are most useful, simple, and popular in the diagrammatic presentation of frequency distributions. These diagrams provides a useful and quick understanding of the shape of the distribution and its characteristics. The basis of comparison in the bar is linear or one-dimensional.’ These diagrams are called one-dimensional diagrams because only the length (height) of the bar (not the width) is taken into consideration. Of course, width or thickness of the bar has no effect on the diagram, even then the thickness should not be too much otherwise the diagram would appear like a two-dimensional diagram.

30. The one-dimensional diagrams (charts) used for graphical presentation of data sets are as follows: Histogram Frequency polygon Frequency curve Cumulative frequency distribution ( Ogive ) Pie diagram

31. The graphic techniques described earlier are used for group frequency distributions. The graphic techniques presented in this section can also be used for displaying values of categorical variables. Such data is first tallied into summary tables and then graphically displayed as either bar charts or pie charts . Simple Bar Charts

32. Bar charts are used to represent only one characteristic of data and there will be as many bars as number of observations. For example, the data obtained on the production of oil seeds in a particular year can be represented by such bars. Each bar would represent the yield of a particular oil seed in that year. Since the bars are of the same width and only the length varies, the relationship among them can be easily established. Sometimes only lines are drawn for comparison of given variable values. Such lines are not thick and their number is sufficiently large. The different measurements to be shown should not have too much difference, so that the lines may not show too much dissimilarity in their heights. Such charts are used to economize space, specially when observations are large. The lines may be either vertical or horizontal depending upon the type of variable—numerical or categorical

33. The frequency polygon is formed by marking the mid-point at the top of horizontal bars and then joining these dots by a series of straight lines. The frequency polygons are formed as a closed figure with the horizontal axis, therefore a series of straight lines are drawn from the mid-point of the top base of the first and the last rectangles to the mid-point falling on the horizontal axis of the next outlaying interval with zero frequency. Frequency Polygon

34. Cumulative Frequency Distribution ( Ogive ) : It enables us to see how many observations lie above or below certain values rather than merely recording the number of observations within intervals. Cumulative frequency distribution is another method of data presentation that helps in data analysis and interpretation. To draw a cumulative ‘less than ogive ’, points are plotted against each successive upper class limit and a corresponding less than cumulative frequency value. These points are then joined by a series of straight lines and the resultant curve is closed at the bottom by extending it so as to meet the horizontal axis at the real lower limit of the first class interval. To draw a cumulative ‘more than ogive ’, points are plotted against each successive lower class limit and the corresponding more than cumulative frequency. These points are joined by a series of Ogive

35. straight lines and the curve is closed at the bottom by extending it to meet the horizontal axis at the upper limit of the last class interval .. Similarly, the perpendicular drawn from the point of intersection of the two curves on the vertical axis will divide the total frequencies into two equal parts.

36. These diagrams are normally used to show the total number of observations of different types in the data set on a percentage basic rather than on an absolute basis through a circle. Usually the largest percentage portion of data in a pie diagram is shown first at 12 o'clock position on the circle, whereas the other observations (in per cent) are shown in clockwise succession in descending order of magnitude. The steps to draw a pie diagram are summarized below: ( i ) Convert the various observations (in per cent) in the data set into corresponding degrees in the circle by multiplying each by 3.6 (360 ÷ 100). ( ii) Draw a circle of appropriate size with a compass . (iii) Draw points on the circle according to the size of each portion of the data with the help of a protractor and join each of these points to the center of the circle. The pie chart has two distinct advantages: ( i ) it is aesthetically pleasing and (ii) it shows that the total for all categories or slices of the pie adds to 100%. Pie Diagram