# ISS (Statistical Services) Statistics Paper III: Questions 40 - 46 of 109

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## Question number: 40

» Applied Statistics » Time Series Analysis » Exponential and Moving Average Smoothing

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Explain moving average [m, p]. Let with p = 1 and m = 2k + 1, obtain the coefficient of and [m, p]

### Explanation

Moving average: moving average method is a simple and flexible method for measuring trend. It consists in measurement of trend by smoothing out the fluctuations of the data by means of a moving average.

The first element of the moving average is obtained by taking the average of the initial fixed subset of the number series i. e. the first average i

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## Question number: 41

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

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Appeared in Year: 2010

### Write in Short

Discuss briefly the steps involved in the construction of cost of living index number.

## Question number: 42

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

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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

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Appeared in Year: 2011

Essay Question▾

### 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.

Align

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## Question number: 44

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Appeared in Year: 2010

Essay Question▾

### 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 sampling:

To draw a sample of s

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## Question number: 45

» Applied Statistics » Index Numbers » Role of CSO

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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 number: 46

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

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Appeared in Year: 2011

Essay Question▾

### 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 its to

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