Structure: 15.1 Introduction Learning Objectives 15.2 Definition of an Index Number Relative Classification of index numbers Base year and current year Chief characteristics of index numbers Main steps in the construction of index numbers 15.3 Methods of Computation of Index Numbers Unweighted index numbers Weighted index numbers 15.4 Tests for Adequacy of Index Number Formulae 15.5 Cost of Living Index Numbers of Consumer Price Index Utility of consumer price index numbers Assumptions of cost of living index number Steps in construction of cost of living index numbers 15.6 Methods of Constructing Consumer Price Index Aggregate expenditure method Family budget method Weight average of price relatives 15.7 Limitations of Index Numbers 15.8 Utility and Importance of Index Numbers 15.9 Summary 15.10 Terminal Questions 15.11 Answers to SAQs and TQs Answers to Self Assessment Questions Answers to Terminal Questions 15.12 References
In the unit 14, ‘Time Series Analysis’, you have studied about the definition and components of time series. You have also studied about different forecasting methods using time series analysis. In this unit 15, ‘Index Sikkim Manipal University Page No. 360
Statistics for Management
Numbers’, we will discuss about the meaning and definition of index numbers, the types of indices along with examples. You will also study about different kinds of index numbers. Finally, you will study about the limitations of index numbers. We know that most values change and therefore we may want to know how much change has taken place over a period of time. For example, we may want to know how much the prices of different items essential to a household have increased or decreased so that necessary adjustments can be made in the monthly budget. However, while price of a few items may have increased, others may have decreased over a given period of time. Consequently, in all such situations, an average measure needs to be defined to compare such difference over a time period. Index numbers are yardsticks for describing such differences. These differences may have to do with the physical quantities of the goods, the prices of the commodities, or such concepts as ‘efficiency’ ‘intelligence’ or beauty’. The comparison may be between the periods of time, between places, between categories and so on. We may have index numbers comparing the cost of living at different times or in different localities or countries. Index numbers are used in comparison of the physical volume of production in different years, or efficiency or different government offices. However, we confine most of our attention to the construction of index numbers measuring changes over time. 15.1.1 Learning Objectives By the end of this unit, you should be able to: Represent a data set in index number form Describe how much the economic variables have changed over time Describe three principal types of indices: price indices, quality indices, and value indices Calculate various kinds of index numbers
15.2 Definition of an Index Number
An index number is a number which is used to measure the level of a certain phenomenon as compared to the level of the same phenomenon at some standard period. In other words, an index number is a number which Sikkim Manipal University Page No. 361
Statistics for Management
is used as a device for comparison between the price, quantity or value of a group of articles in different situations, for example, at a certain place or a period of time and that of another place or period of time. Key Statistic An index number is a statistical measure which is designed to express changes or differences in a variable or a group of related variables. It is usually expressed in percentage form. When a comparison is in respect of prices, it is called an index number of price, when in respect of physical...