# Applied Statistics-Index Numbers (ISS 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 factor-reversal 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 Distribution-Pareto and Engel Curves

Appeared in Year: 2009

Essay Question▾

### 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… (250 more words) …

## Question number: 7

» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number

Appeared in Year: 2009

Essay Question▾

### 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 Equation 1 1 Equation 10 5 Equation 2 x Equation 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

Essay Question▾

### 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.

1. Formula error

2. Sampling error

3. 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… (224 more words) …

## Question number: 10

» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives

Appeared in Year: 2010