# Applied Statistics (ISS (Statistical Services) Statistics Paper III): Questions 20 - 25 of 45

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## Question number: 20

» 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

## Question number: 21

» Applied Statistics » Time Series Analysis » Exploratory Time Series Analysis

Appeared in Year: 2011

### Describe in Detail

Give the various steps for finding the variance of the random component using variate difference method. Is F-test used for testing the significance of homogeneity of two successive estimates of variance? If yes, ok, otherwise which ’test can be used? Discuss.

### Explanation

To find the variance of the random component using variate difference method:

let us consider a series represented as the sum of functional part and random component

Here are considered as independently identically distributed with

…. (i)

for a plynomial of m^{th} degree

## Question number: 22

» 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: 23

» 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

## Question number: 24

» 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

## Question number: 25

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2012

### Describe in Detail

What are the different methods for measurement of trend? Discuss the method of fitting a straight line using least squares method.

### Explanation

**Methods of measurement of trend: **

Trend can be measured by the following methods:

(i) Graphic method or trend by Inspection

(ii) Method of Semi-Averages

(iii) Method of Curve fitting by principles of Least Squares

(iv) Method of moving averages

**Fitting a straight line using least squares method: **

Let be