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Problems on Construction of Index Numbers, Business Mathematics and Statistics | Business Mathematics and Statistics - B Com PDF Download

There are several problems that a statistician encounter in process of construction of Index Numbers. These are as follows—


(1) A clear definition of the purpose for which the index is constructed should be made. Before collection of data for construction of index numbers, it is of utmost importance to know what is the purpose for construction of index numbers. For example if we wish to measure trend in price changes with a view point of finding the consumption pattern of a household; in such a case we should take retail prices and not wholesale prices of items into consideration.


(2) Selection of number of items. Those items which are relevant for a partiality type of changes are to be selected, for example in computing the cost of living index Number of a middle class family gold will not be a relevant item, where as family clothing should be included.


(3) Base period - Base period is a reference period whose level of prices (in case of Price Index) represents the base from which changes in prices are measured. For example when we compare the prices of wheat in the year 2008 with that of 2000, the year 2000 is the base year.
The choice of base period is very critical in construction of Index Numbers and it is based on the following two considerations-

(a) base year should be a normal period i.e. period with relative stability and should not be affected by extraordinary events like war, famine etc.

(b) It should not be in too distant past.
The choice is also to be made about the kind of base to be used i.e. whether fixed base should be used or chain base should be used.


(4) Selection of weights - Weights imply the relative importance of the different variables. It is very essential to adopt a suitable method of weighting to avoid arbitrary & haphazard weights. For instance, in computing cost of living index, wheat or rice should be given more importance as compared to sugar or salt.


(5) Adoption of suitable formula for construction of index number- As there are number of formulas to calculate index number ; most appropriate & proper one should be used & selected depending upon the circumstances.

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FAQs on Problems on Construction of Index Numbers, Business Mathematics and Statistics - Business Mathematics and Statistics - B Com

1. What are index numbers in business mathematics and statistics?
Ans. Index numbers in business mathematics and statistics are statistical measures used to express changes in a group of related variables over time. They provide a way to compare different data sets by setting a base period or base value as a reference point.
2. How are index numbers constructed?
Ans. Index numbers are constructed by selecting a base period or base value, which is assigned a value of 100. The values of the variables in subsequent periods are then compared to the base period or base value and expressed as a percentage change. This percentage change is used to construct the index number.
3. What are the problems encountered in the construction of index numbers?
Ans. There are several problems encountered in the construction of index numbers, such as the selection of an appropriate base period, the choice of variables to include, the treatment of missing data, and the weighting of different variables. These problems can affect the accuracy and reliability of the index numbers.
4. How do you deal with missing data when constructing index numbers?
Ans. When dealing with missing data in the construction of index numbers, there are several methods that can be employed. One common approach is to estimate the missing values using interpolation or extrapolation techniques. Another method is to exclude the missing data from the calculations, but this may lead to biased results.
5. What is the importance of index numbers in business mathematics and statistics?
Ans. Index numbers play a crucial role in business mathematics and statistics as they provide a way to measure and analyze changes in variables over time. They are used in various fields such as economics, finance, and market research to track trends, make comparisons, and make informed decisions. Index numbers help in understanding the relative changes in different data sets and serve as valuable tools for forecasting and planning.
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