# ISS (Statistical Services) Statistics Paper III: Questions 43 - 48 of 109

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## Question 43

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Appeared in Year: 2011

### Describe in Detail

Essay▾

Explain aligned sample and unaligned systematic sampling method

### Explanation

Systematic sampling in two dimensions:

The linear systematic sampling can be extended for two dimensions populations. here it is assumed that the n m k l population units are arranged in the form of ml rows, each containing nk units and a systematic sampling of m n units is selected. There are two procedures adopted to draw a sample of size mn.

Align&#8230;

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## Question 44

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Appeared in Year: 2010

### Describe in Detail

Essay▾

Explain the concepts of linear and circular systematic sampling giving suitable illustrations.

Further, show that for linear systematic sampling, sample mean is an unbiased estimator for population mean.

### Explanation

Let us suppose that N sampling units are serially numbered from 1 to N in some order and a sample of size n is to be drawn in such a way that N is expressible as a product of two integers n and k.

N = nk ⇾ k = Where k, usually called the sampling interval. k is taken as the integer nearest to

Linear systematic sampling:

To draw a sample of size n, s&#8230;

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## Question 45

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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 46

Income Distribution-Pareto and Engel Curves
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Appeared in Year: 2011

### Describe in Detail

Essay▾

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 its to&#8230;

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## Question 47

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Appeared in Year: 2011

### Describe in Detail

Essay▾

Discuss Lahiri՚s method of selecting samples for PPS scheme. Give a suitable example to select

4 units when N = 10, M = 60, by taking your choice of sample number and its corresponding size.

### Explanation

Lahiri՚s Method of selecting samples for PPS scheme:

Let M = max maximum of the sizes of N units in the population (i = 1,2, … 10)

Steps involved in selecting samples:

1) Select a random number i from 1 to N

2) Select one more random number j, such that

3) If , then ith unit is selected, otherwise the pair (i, j) is rejected and another pair is chosen&#8230;

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## Question 48

Income Distribution-Pareto and Engel Curves
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Appeared in Year: 2011

### Describe in Detail

Essay▾

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) Determination 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 income is&#8230;

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