# Applied Statistics-Index Numbers (ISS (Statistical Services) Statistics Paper III): Questions 11 - 17 of 25

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## Question number: 11

» Applied Statistics » Index Numbers » Role of CSO

Appeared in Year: 2010

### Write in Short

What is C. S. O. ? Describe briefly the role and importance of C. S. O. for execution of Indian statistical data.

## Question number: 12

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2011

### Describe in Detail

Explain curve of concentration. Obtain income concentration for Pareto’s law of income distribution.

### Explanation

curve of concentration:

A concentration curve plots two variables p and q of the distribution income.

In case the form of the income distribution ϕ (x) is not known then with the help of curves of concentration, we can make a useful formulation of the problem of distribution of income.

Let N be the total frequency of the population and I be the

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## Question number: 13

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2011

### Describe in Detail

Explain the formulation of the problem of distribution of income. Further discuss its Mathematical formulation in order to find number of persons with income x or more.

### Explanation

Formulation of the problem of distribution of income:

The problem of distribution of income can be formulated as follows

(a) Determation of the form of the frequency distribution ϕ (x), for the total distribution of income from the poorest to the richest members of the society.

(b) Check whether ϕ (x) is governed by the society from which in

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## Question number: 14

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

Appeared in Year: 2010

### Write in Short

What are the three tests of index numbers? Verify whether the following index number satisfies any of these tests:

I=

Where L = Lasperaye’s Price Index Number

P = Paasche’s Price Index Number.

## Question number: 15

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2013

### Describe in Detail

Explaining Pareto’s law of income distribution, show that the elasticity decreases in the number of persons while passing to a higher income class.

### Explanation

**Pareto’s law of income distribution: **

Pareto’s states that ‘the number of income recipients earning at least a given level of income would tend to fall by a fixed percentage as that given level of income rose by a fixed percentage. ’

Pareto’s law implies that inequality is inescapable and nothing coiuld be done about it.

pareto’s law is only tru

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## Question number: 16

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2013

### Describe in Detail

Discuss Engel’s curve. Explain the Engel’s curve for constant price of a demand functionwhere is national income and p is price.

### Explanation

**Engel’s curve: ** The graphic representation of the basic relationship between household income and its expenditure on a particular item of consumption is known as Engel’s curve. The Engel curves shows the effect of a change in income on the expenditure for each good at fixed prices. If price change, the result will be shift in each of the Engel cur

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## Question number: 17

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

### Describe in Detail

Discuss simple aggregate method of Index number. Why is weighted average of price relative index preferred over simple aggregate method? Show that weighted average of price relative index number is same as that of Paasche’s index number.

### Explanation

**Simple aggregate method of Index number: **

This method consists of expressing aggregate of prices in any year as a percentage of their aggregate i^{th} the base year. The price index, under this method is computed by the formula

Where

= Price index of the current year with reference to the base year

= Total of the prices of the cu

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