# ISS (Statistical Services) Statistics Paper III: Questions 42 - 48 of 109

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## Question number: 42

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2010

### Write in Short

Discuss the ratio to trend method for separating the seasonal component in a time series.

## Question number: 43

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2011

### Describe in Detail

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.

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## Question number: 44

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

### Describe in Detail

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 sampli**

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## Question number: 45

» 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: 46

» 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: 47

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2011

### Describe in Detail

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 i^{th} unit is selected, otherw

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## Question number: 48

» 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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