# ISS (Statistical Services) Statistics Paper III: Questions 66 - 73 of 109

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## Question number: 66

» Applied Statistics » Index Numbers » Laspeyre

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Why do the errors occur in the measurement of price and quantity index numbers? Give the names of those errors.

### Explanation

Errors in the measurement of price and quantity index numbers:

Generally, index numbers for prices are constructed from m commodities, which are common to both the base year and the given year. But in practical calculations, it may not be possible to consider all common commodities say, M.

Therefore, value index

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## Question number: 67

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Appeared in Year: 2012

### Write in Short

Let be the y-value of the ith unit and be corresponding selection probability,

i = 1,2, …, N. Then, based on a sample of size n drawn with replacement, show that an unbiased estimator for population total is

## Question number: 68

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

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Explain the following:

(i) Weighted Aggregates method

(ii) Criteria of a good index number

### Explanation

(i) Weighted Aggregates Method:

In this method, an index number of prices for any given year is calculated after assigning the appropriate weights to the different items included in that index number.

Usually weights are assigned on the basis of quantities, values or sale price of the commodities consumed during the base year or in some typical

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## Question number: 69

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Appeared in Year: 2012

### Write in Short

Discuss forecasting accuracy and Theil’s U coefficient.

## Question number: 70

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

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Appeared in Year: 2012

### Write in Short

Using curves of concentration, discuss the formulation of the problem of distribution of income.

## Question number: 71

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Appeared in Year: 2012

### Write in Short

Obtain the general solution of first-order auto-regression model.

## Question number: 72

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Discuss the relevance of variate difference method in time series analysis data. Show that

### Explanation

Relevance of variate difference method:

Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does not require the specification of a

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## Question number: 73

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Explain circular systematic sampling. Show that minimum value of ρ is , when , where ρis intraclass correlation and is the sample mean.

### Explanation

Circular systematic sampling

This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every kth unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to .

That is, if r is the number selected at random from 1 to N, the

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