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.