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

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## Question 66

Appeared in Year: *2013*

### Describe in Detail

Essay▾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 can be either in terms of M commodit…

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## Question 67

Appeared in Year: *2012*

### Write in Short

Short Answer▾Let be the *y*-value of the i^{th} 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 68

Appeared in Year: *2013*

### Describe in Detail

Essay▾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 years…

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## Question 69

Appeared in Year: *2012*

### Write in Short

Short Answer▾Discuss forecasting accuracy and Theil՚s U coefficient.

## Question 70

Appeared in Year: *2012*

### Write in Short

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

## Question 71

Appeared in Year: *2012*

### Write in Short

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

## Question 72

Appeared in Year: *2013*

### Describe in Detail

Essay▾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 ri…

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## Question 73

Appeared in Year: *2013*

### Describe in Detail

Essay▾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 k^{th} 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 sample consists o…

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