Applied StatisticsIndex Numbers (ISS (Statistical Services) Statistics Paper III): Questions 5  10 of 25
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Question number: 5
» Applied Statistics » Index Numbers » Link and Chain Relatives Composition of Index Numbers
Appeared in Year: 2009
Write in Short
Explain the time reversal and factorreversal tests for an ideal index number. Give an example
of index number which satisfies both of these tests.
Question number: 6
» Applied Statistics » Index Numbers » Income DistributionPareto and Engel Curves
Appeared in Year: 2009
Describe in Detail
State the probability density function of the Pareto distribution and give its cumulative form.
Interpret the constants involved.
Explanation
Probability Density Function of the Pareto distribution:
Suppose that X has the Pareto distribution with shape parameter a∈ (0, ∞) and scale parameter b∈ (0, ∞) then X has probability density function f given by
where is the (necessarily positive) minimum possible value of X, and α is
Question number: 7
» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number
Appeared in Year: 2009
Describe in Detail
Define Marshall Edgeworth index number and examine whether it satisfies Fisher’s tests for index numbers. Also show that this index number will lie between the Laspeyres’ and Paasche’s index numbers.
Explanation
Marshall Edgeworth Index Number:
In this index number, the average of the quantities of the base year and current year are used as weights. Thus, the weight of an item would be . Accordingly the formula of index number is:
= X 100
OR
=
Question number: 8
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2011
Write in Short
For the following table:
Commodity
A  B  
 1  1 
 10  5 
 2  x 
 5  2 
Where p and q stand for price and quantity for 0 and 1 time periods respectively. Find the value of X if the ratio between Laspeyre’s (L) and Paasche’s (P) index number is L: P: : 28: 27
Question number: 9
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2011
Describe in Detail
Explain the errors in the measurement of price and quantity index number.
Explanation
All index numbers are affected by mainly three types of errors.

Formula error

Sampling error

Homogeneity error
Formula error:
There is no universally accepted index number formula that will measure the price or quantity changes excatly. Each formula in common use has its own defeat and consequently some error is
Question number: 10
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2010
Write in Short
Discuss briefly the steps involved in the construction of cost of living index number.