# Applied Statistics (ISS (Statistical Services) Statistics Paper III): Questions 26 - 32 of 45

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## Question number: 26

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

### 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 i^{th} the base year. The price index, under this method is computed by the formula

Where

= Price index of the current year

## Question number: 27

» Applied Statistics » Periodogram and Correlogram Analyses

Appeared in Year: 2012

### 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,

## Question number: 28

» 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: 29

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

### 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,

## Question number: 30

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

Appeared in Year: 2013

### 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

## Question number: 31

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

Appeared in Year: 2012

### Write in Short

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

## Question number: 32

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

Appeared in Year: 2013

### 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