# ISS Statistics Paper III: Questions 60 - 65 of 90

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## Question number: 60

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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… (224 more words) …

## Question number: 61

Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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,… (60 more words) …

## Question number: 62

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

Appeared in Year: 2012

### Write in Short

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

## Question number: 63

Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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… (233 more words) …

## Question number: 64

Appeared in Year: 2012

### Write in Short

Show that for a simple random sample unbiased estimate of

## Question number: 65

Appeared in Year: 2012