CDG1A/CDZ3A/CDC3A/ MBT3A BUSINESS STATISTICS. Unit : I - V

Transcription

1 CDG1A/CDZ3A/CDC3A/ MBT3A BUSINESS STATISTICS Unit : I - V 1

2 UNIT I Introduction Meaning and definition of statistics Collection and tabulation of statistical data Presentation of statistical data Graphs and diagrams CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 2

3 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 3

4 DEFINITION STATISTICS AS NUMERICAL DATA By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other. - PROF.HORACE SECRIST STATISTICS AS STATISTICAL METHODS The science which deals with the collection, analysis and interpretation of numerical data. - CROXTON AND COWDEN CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 4

5 FUNCTIONS OF STATISTICS Statistics presents the fact in definite form It simplifies mass of data. It facilitates for comparison. It facilitates in formulating policies It tests hypothesis It measures the trend behaviour LIMITATIONS OF STATISTICS Statistical methods does not study individuals. Statistics laws are true only on an average. Statis tical methods are not suited to study qualitative data. If sufficient care is not exercised in collecting, analyzing and interpretation the data, statistical results might be misleading. Only a person who has an expert knowledge of statistics can handle statistical data efficiently. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 5

6 SCOPE OF STATISTICS Statistics in Business Statistics in Economics Statistics in Mathematics Statistics in Banking Statistics in Administration Statistics in Accounting and Auditing Statistics in Natural and Social Sciences Statistics in Astronomy CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 6

7 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 7

8 COLLECTION OF DATA DATA PRIMARY DATA SECONDARY DATA CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 8

9 METHODS OF COLLECTING PRIMARY DATA DIRECT PERSONAL INTERVIEWS INDIRECT ORAL INTERVIEWS INFORMATION FROM CORRESPONDENTS MAILED QUESTIONNAIRE METHOD SCHEDULES SENT THROUGH ENUMERATORS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 9

10 SOURCES OF SECONDARY DATA Published Sources: Official publications of Central and local governments. Official publications of semi government statistical organization. Official publication of foreign government or international bodies like the UNO, World Bank, ADB, WTO, UNESCO, etc. Reports and publications of Trade union, Chamber of Commerce, Commercial Banks, Co-operatives, Stock Exchange etc. Report submitted to economists, re-search scholars, universities and various educational and research institutions. Reports of various committees and commissions appointed by government. Newspaper and Periodicals. CDG1A/CDZ3A/CDC3A/MBT3A CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS BUSINESS STATISTICS STATISTICS 10

11 Unpublished Sources: The statistical data needn t always be published. There are various sources of unpublished statistical material such as the records maintained by Private firms Business enterprises Scholars Research workers, etc. They may not like to release their data to any outside agency. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 11

12 CLASSIFICATION OF DATA CLASSIFICATION TYPES GEOGRAPHICAL CHRONOLOGICAL QUALITATIVE QUANTITATIVE CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 12

13 TABULATION TM Tabulation is the process of condensing classified data in the form of a table so that it may be more easily understood and so that any comparisons involved may be more readily made. TYPES OF TABLES CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 13

14 REPRESENTATION OF DATA TYPES OF DIAGRAMS ONE DIMENSIONAL OR BAR DIAGRAMS TWO DIMENSIONAL OR AREA DIAGRAMS THREE DIMENSIONAL OR VOLUME DIAGRAMS PICTOGRAMS AND CARTOGRAMS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 14

15 TYPES OF DIAGRAMS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 15

16 TYPES OF GRAPHS HISTOGRAM FREQUENCY POLYGON FREQUENCY CURVE OGIVES 16 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 16

17 MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN MEDIAN MODE HARMONIC MEAN GEOMETRIC MEAN MEASURES OF VARIATION RANGE QUARTILE DEVIATION MEAN DEVIATION STANDARD DEVIATION MEASURES OF SKEWNESS UNIT II SYMMETRICAL DISTRIBUTION POSITIVELY SKEWED DISTRIBUTION NEGATIVELY SKEWED DISTRIBUTION CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 17

18 MEASURES OF CENTRAL TENDENCY MEANING A CENTRAL VALUE IS A SINGLE VALUE WHICH DESCRIBES THE CHARCTERISTICS OF THE ENTIRE DATA. MEASURES ARITHMETIC MEAN MEDIAN MODE HARMONIC MEAN GEOMETRIC MEAN CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 18

19 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 19

20 ARITHMETIC MEAN Arithmetic mean is usually called as average and is given by sum of all observations divided by the total number of observations given. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 20

21 ARITHMETIC MEAN MEAN GEOMETRIC MEAN x = HARMONIC MEAN CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 21

22 MEDIAN The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 22

23 MODE CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 23

24 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 24

25 For various methods of calculating mean, median, mode for different types of data, follow the links CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 25

26 MEASURES OF DISPERSION The average measures the center of the data. Another feature of the observation is how the observations are spread about the center. The observations may be close to the center or they may be spread away from the center. If the observations are close to the center (usually the arithmetic mean or median), we say that dispersion, scatter or variation is small. If the observations are spread away from the center, we say dispersion is large. RANGE QUARTILE DEVIATION MEAN DEVIATION STANDARD DEVIATION TYPES CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 26

27 MEASURES OF DISPERSION ABSOLUTE MEASURE OF DISPERSION : It measures the distribution in original units of data. Variability in two or more series can be compared, provides they are in the same unit and same average. RELATIVE MEASURE OF DISPERSION : It is free from unit of measurement of data. It is the ratio of the measure of absolute dispersion to the average, from which absolute deviations are made. It is called as coefficient of variation CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 27

28 For formulae, merits and demerits of various measures of dispersion refer CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 28

29 MEASURES OF SKEWNESS Skewness is a term in statistics used to describes asymmetry from the normal distribution in a set of statistical data. Skewness can come in the form of negative skewness or positive skewness, depending on whether data points are skewed to the left and negative, or to the right and positive of the data average. A dataset that shows this characteristic differs from a normal bell curve. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 29

30 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 30

31 METHODS OF STUDYING SKEWNESS Sub Code - Sub Name 31

32 UNIT III CORRELATION ANALYSIS DEFINITION AND TYPES SCATTER DIAGRAM METHOD KARL PEARSON METHOD SPEARMAN S RANK CORRELATION REGRESSION ANALYSIS REGRESSION EQUATIONS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 32

33 CORRELATION Correlation is a statistical method used to study the relationship between two or more variables. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 33

34 CORRELATION AND CAUSATION Causation implies correlation. But correlation does not always imply causation. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 34

35 TYPES OF CORRELATION A. Positive and Negative Correlation Positive Correlation: If the two variables vary in the same direction i.e., if both the variables increase or decrease in the same direction then there exists a positive correlation. Eg : Income and expenditure Negative Correlation: If the two variables vary in the opposite direction i.e., if one variable increases the other decreases or vice versa, then there exists a negative correlation. Eg : No of men and work CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 35

36 Linear Correlation: Example LINEAR AND NON-LINEAR CORRELATION The ratio of change in between the variables is the same. Non-Linear Correlation: The amount of change in one variable does not bear a constant ratio to the amount of change in the other variable. Example: X Y If the amount of rainfall is doubled, the yield of a crop is not necessarily doubled. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 36

37 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 37

38 METHODS OF STUDYING CORRELATION Scatter diagram method. Karl Pearson s method. Spearman s Rank Correlation method. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 38

39 SCATTER DIAGRAM METHOD Scatter diagram is a graphical method of finding correlation. It is one of the simplest procedures to judge correlation between variables. One variable is taken along the x- axis and other variable is taken along the y-axis. From the plotted points, we can find whether the variables are correlated or not. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 39

40 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 40

41 KARL PEARSONS METHOD Karl Pearson s Coefficient of Correlation is widely used mathematical method wherein the numerical expression is used to calculate the degree and direction of the relationship between linear related variables. Pearson s method, popularly known as a Pearsonian Coefficient of Correlation, is the most extensively used quantitative methods in practice. The coefficient of correlation is denoted by r. For example refer, CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 41

42 RANK CORRELATION This method is based on Ranks. It is useful when the data is of qualitative nature like honesty, efficiency, intelligence, beauty etc., The rank correlation coefficient is given by 2 D ρ = 1 2 N( N 1) Where N is the number of observations and D is the difference between number of observations CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 42

43 REGRESSION Regression is a statistical method which is used to estimate the unknown value of one variable using known value of other variable, provided the variables are correlated. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 43

44 REGRESSION EQUATIONS Regression Line of X on Y: Regression Line of Y on X : CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 44

45 DIFFERENCE BETWEEN CORRELATION AND REGRESSION CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 45

46 UNIT IV TIME SERIES ANALYSIS MEANING AND DEFINITION COMPONENTS OF TIME SERIES METHODS OF MEASURING TREND METHODS OF MEASURING SEASONAL VARIATION CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 46

47 TIME SERIES CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 47

48 MEANING A time series is a set of observations arranged in chronological order. DEFINITIONS A time series consists of statistical data which are collected, recorded and observed over successive increments. When quantitative data are arranged in the order of their occurrence, the resulting series is called a time series. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 48

49 EXAMPLES The hourly series of temperature recorded. The weekly series of attendance in a company. The monthly series of steel production. The annual series of national income. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 49

50 COMPONENTS OF TIME SERIES The factors that are responsible for bringing about changes in a time series are called the components of time series. SECULAR TREND SEASONAL VARIATIONS CYCLICAL VARIATIONS IRREGULAR VARIATIONS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 50

51 SECULAR TREND The secular trend refers to the general direction and movement of time series. EXAMPLES. UPWARD TREND : The series concerning Population, national income, bank deposits etc. DOWNWARD TREND : Series concerning death rates specially in deaths by epidemics etc. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 51

52 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 52

53 SEASONAL VARIATIONS Seasonal variations refer to a recurrent pattern of change within the period due to climate or custom at different periods of time. EXAMPLES In each year more ice creams sold during summer and less in winter. More woolen clothes are sold during winter and less in summer. Increase in sales of garments in festive seaons. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 53

54 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 54

55 CYCLICAL VARIATIONS Cyclical variations are oscillatory movements in a time series with period of oscillation greater than one year. Cyclical movements are defined as up and down movements which are different from seasonal fluctuations because they extend over longer period of time. The cyclical fluctuations are not necessarily uniformly periodic. A cycle (one complete period) normally lasts from 7 to 9 years. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 55

56 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 56

57 IRREGULAR VARIATIONS Irregular variations are fluctuations in time series that are short in duration, erratic in nature and follow no regularity in the occurrence pattern. These variations are usually caused by nonrecurring factors like floods, wars, earthquakes, strikes and lock-outs, epidemics etc. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 57

58 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 58

59 METHODS OF MEASURING TREND FREE HAND OR GRAPHIC METHOD METHOD OF SEMI AVERAGES. METHOD OF MOVING AVERAGES. METHOD OF LEAST SQUARES. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 59

60 METHODS OF MEASURING SEASONAL VARIATIONS METHOD OF AVERAGES MOVING AVERAGES METHOD RATIO TO MOVING AVERAGE METHOD RATIO TO TREND METHOD FOR PROBLEMS, REFER CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 60

61 UNIT V INDEX NUMBERS TYPES OF INDEX NUMBERS AGGREGATIVE AND RELATIVE INDEX CHAIN AND FIXED INDEX WHOLESALE INDEX COST OF LIVING INDEX STATISTICAL QUALITY CONTROL CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 61

62 INDEX NUMBERS Index numbers are developed for measuring the effect of change in prices. They are described as barometers of economic activity. DEFINITIONS : Index numbers are devices for measuring differences in the magnitude of a group of related variables Croxton and Cowden. An index number is nothing more than a relative number which expresses the relation between two figures, which one of them is used as a base. - Morris Hamberg. It is a numerical value characterizing the change in complex economic phenomena over a period of time or space Maslow. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 62

63 USES OF INDEX NUMBERS Index numbers measure the economic and business behaviour, and is called the barometers of economic activity. The primary purpose of index numbers is to measure the relative temporal or cross sectional changes in a variable or set of variables over some base figure. Management for any organization uses index numbers for efficient planning and formulation of business policies. Index numbers are specially used to study the general trend for a time series data. They can be used to forecast future events. The cost of living index numbers help in computing real wages. Index numbers are used to for deflating net national product or income calculated at current prices. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 63

64 TYPES OF INDEX NUMBERS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 64

65 1. PRICE INDEX This compares the prices of a group of commodities at a certain time or place with prices of the base period or place respectively. 2. QUANTITY INDEX This index measures the changes in the volume of goods produced, purchased or consumed Eg : indices of agricultural production, industrial production, imports, exports etc. 3. VALUE INDEX : This index compares the total value of some period with the total value of the base period. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 65

66 METHODS OF CONSTRUCTING INDEX NUMBERS CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 66

67 UNWEIGHTED INDICES SIMPLE AGGREGATIVE METHOD : p 1 P 01 = x 100 p 0 SIMPLE AVERAGE OF PRICE RELATIVE METHOD : (Using Arithmetic Mean) P 01 = (Using Geometric Mean ) p p o N log P P 01 = antilog x 100 N CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 67

68 WEIGHTED INDEX NUMBERS WEIGHTED AGGREGATIVE INDICES LASPEYRE S INDEX Laspeyres index P = p q 1 o 01 p o q o 100 PAASCHE S INDEX Paasche s index CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 68

69 FISHER S IDEAL INDEX : BOWLEY S INDEX : MARSHALL EDGEWORTH METHOD: CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 69

70 WEIGHTED AVERAGE OF RELATIVES 1. Using arithmetic mean, PV P 01 = V 2. Using geometric mean, V log P P 01 = Antilog , V = p 0 q 0 V For example, refer CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 70

71 QUANTITY INDEX NUMBERS Quantity indices are obtained by changing p to q and q to p in the various formulas. VALUE INDEX NUMBERS The value of a single commodity is the product of its price and quantity. p 1 q 1 V 01 = x 100 p 0 q 0 CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 71

72 TESTS OF ADEQUACY To know about the various tests for index numbers and the list index numbers which satisfy the tests, refer CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 72

73 Chain Base And Fixed Base TM Indices CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 73

74 CONSUMER PRICE INDEX Consumer price index numbers is also known as cost of living index numbers, are generally intended to represent the average change overtime in the prices paid by the ultimate consumer of a specified basket of goods and services. METHODS: Aggregate Expenditure Method Family Budget Method For problems refer CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 74

75 Statistical Quality Control Statistical quality control refers to the use of statistical methods in the monitoring and maintaining of the quality of products and services. It uses graphical displays known as control charts to determine whether a process should be continued or should be adjusted to achieve the desired quality. CDG1A/CDZ3A/CDC3A/MBT3A BUSINESS STATISTICS 75