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…

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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…

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Question 45

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Appeared in Year: 2010

Write in Short

Short Answer▾

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

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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…

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Question 47

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Appeared in Year: 2011

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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…

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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…

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