The following are the difficulties encountered during the construction of consumer price index:

• Index numbers are not based on all items: As index numbers are generally based on a couple of sample, it is not possible to take into account each and every item in the construction of index.
• Index numbers are not free from error: In every stage of the construction of index numbers, starting from selection of commodities to the choice of formula there is a chance an error being introduced.
• It is also said that, index numbers are also special type of averages, since the various averages like mean, median and mode and have their relative limitations which may lead to some errors.
• Index numbers are meant for a particular purpose: An index number is used to measure the change for a particular purpose only.
• Prices used in the construction of cost of living index are retail prices, which vary from shop to shop, place to place and consumer to consumer. Therefore, index numbers prepared on such prices cannot be used for different places or different classes of people.
• Index numbers include so many commodities of unstable quality, which can not be used at different points of time. 
• The ratio of expenditure on different products at different points of time and by various persons are not same and they create difficulties in the construction of cost of living index numbers.