# ISS (Statistical Services) Statistics Paper III: Questions 60 - 65 of 109

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## Question 60

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Appeared in Year: 2013

### Describe in Detail

Essay▾

Discuss simple aggregate method of Index number. Why is weighted average of price relative index preferred over simple aggregate method? Show that weighted average of price relative index number is same as that of Paasche՚s index number.

### Explanation

Simple aggregate method of Index number:

This method consists of expressing aggregate of prices in any year as a percentage of their aggregate ith the base year. The price index, under this method is computed by the formula

Where

= Price index of the current year with reference to the base year

= Total of the prices of the current year

= Total of the&#8230;

… (199 more words) …

## Question 61

Appeared in Year: 2012

### Describe in Detail

Essay▾

Obtain the correlogram for the series with , provided , , and successive values of are independent .

### Explanation

It is given that

And hence

Substituting the value in we get,

Where ηs are independent.

Multiplying both sides of the above equation by , taking expectations and dividing by , we get for a long series,

… (i)

Which is a (homogeneous) linear difference equation of order 2 in the trial solution gives

is the general solution of (i) , A and B being arbit&#8230;

… (21 more words) …

## Question 62

Income Distribution-Pareto and Engel Curves
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Appeared in Year: 2012

### Write in Short

Discuss Engel ′ s law and Engel ′ s curve. Explain Engel ′ s curve for constant price.

## Question 63

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Appeared in Year: 2012

### Describe in Detail

Essay▾

Discuss the allocation of a sample to different strata in stratified sampling. Explain proportional allocation and hence obtain the variance of mean of a stratified sample under proportional allocation.

### Explanation

For a population consisting of N sampling units it can be divided into k relatively homogeneous sub-groups of sizes , , … , (called as strata) such that N = .

Then a simple random sample of size (i = 1,2, … , k) is drawn from each of the stratum such that n = , and this sample is the stratified random sample of size n .

Allocation of a sample to d&#8230;

… (184 more words) …

## Question 64

Appeared in Year: 2012