# Applied Statistics (ISS (Statistical Services) Statistics Paper III): Questions 33 - 39 of 45

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## Question number: 33

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2012

### Describe in Detail

Discuss link relative method to estimate seasonal fluctuations, with appropriate illustrations.

### Explanation

link relative is the value of one season expressed as a percentage of the preceding season. The word ‘season’ refers to time period, it means month for monthly data, quarter for quarterly data etc.

Under this method, the seasonal indices are found with the following steps.

**Steps: **

(i) Find the link relative of all the seasonal data using the fo

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## Question number: 34

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2013

### Describe in Detail

Discuss various steps of finding adjusted monthly indices of seasonal variations using link relative method.

### Explanation

**Steps of finding adjusted monthly indices of seasonal variations using link relative method: **

(i) Find the link relative of all the seasonal data using the formulae

Where = link relative of the current season

(ii) Arrange the entire link relatives thus obtained seaso

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## Question number: 35

» Applied Statistics » Index Numbers » Demand Analysis

Appeared in Year: 2014

### Describe in Detail

Define price elasticity of demand and income elasticity of demand. Point out their uses in economic analysis.

### Explanation

**Price elasticity of demand: **

Price elasticity of demand is a measure of the relationship between a change in the quantity demanded of a particular good and a change in its price.

Price elasticity of demand shows the sensitiveness or responsiveness of demand to the change in price.

Price elasticity of demand is defined as the value of the ratio o

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## Question number: 36

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2014

### Describe in Detail

Define Laspeyres’ and Paasche’s index numbers. It is sometimes stated that Laspeyres’ price index number tends to overestimate price changes while Paasche’s price index number tends to underestimate them. Justify or refute the above statement giving reasons.

### Explanation

**Laspeyre’s Index Number: **

Laspeyre’s index number is a index number where the base year quantities are taken as weights. Under this method, we get the weighted index on the basis of aggregative expenditure, assuming that the quantities consumed in the base year are also the quantities consumed in the current year.

where

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## Question number: 37

» Applied Statistics » Time Series Analysis » Illustration, Additive and Multiplicative Models

Appeared in Year: 2014

### Describe in Detail

What are the two mathematical models employed for time series analysis? Can one model be considered as a particular type of the other one? Which one of the two models is considered to be more useful and why? Discuss each of the above aspects.

### Explanation

The two mathematical models employed for time series analysis:

(i) Additive model

(ii) Multiplicative Model

**Additive model: **

According to the additive model the time series can be expressed as

where

is the time series value at time T

Represents the Trend value

Represents the Seasonal value

Represents the Cyclic value

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## Question number: 38

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

Appeared in Year: 2014

### Describe in Detail

Discuss how you will proceed for constructing a cost of living index number for a given expenditure group in a city.

### Explanation

**Steps involved in the construction of cost of living index number. **

**i) Scope and coverage**: Since it is always constructed for a particular community, first step is to specify the particular class of people for which the index number is going to be constructed. such class may be industrial workers of a particular locality, government employees of a

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## Question number: 39

» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number

Appeared in Year: 2014

### Describe in Detail

Define Fisher index number. Show why Fisher index number is said to be ideal index number. Also, show why Laspeyres’ and Paasche’s index number are not ideal one.

### Explanation

Fisher’s index number:

Fisher’s index number is the geometric mean of laspeyer’s and Paasche’s index number. This index number uses bith base and current year quantities as weights. It counter balances the effect of upward and downward bias experienced with the method os Laspeyer’s and Paasche’s by taking into account both the current year’s and

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