# ISS (Statistical Services) Statistics Paper III: Questions 76 - 81 of 109

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## Question number: 76

» Sampling Techniques » Simple Random Sampling and Sampling with Probability Proportional to Size

Appeared in Year: 2013

### Describe in Detail

In simple random sampling without replacement (SRSWOR), the sample mean ** ** is an unbiased estimator of population mean ** .** Obtain the variance of the estimator of the population total Y.

### Explanation

Sample mean is an unbiased estimator of population mean i. e.

Sample mean is given by

It can also be written as

Where

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## Question number: 77

» 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 formulae

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## Question number: 78

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2013

### Describe in Detail

Give the names of various procedures for selecting a sample using probability proportional to size (PPS) scheme. Obtain an unbiased estimator of the population mean under PPS.

### Explanation

**Procedures for selecting a sample using probability proportional to size (PPS) scheme are:**

PPS sampling with Replacement

PPS sampling without Replacement

Cumulative total method

Lahiri’s method

**An unbiased estimator of the population mean under PPS:**

Let = value of the ith unit of the population, i = 1,2, …, N

= known value of the auxiliary varia

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## Question number: 79

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2012

### Write in Short

Let the demand function be expressed as . For what value of X, the elasticity of demand will be unitary?

## Question number: 80

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2013

### Describe in Detail

Describe the principles of stratification. Explain how the allocation of sample size in different strata is made.

### Explanation

**Principles of stratification:**

The principle of stratification is the division of the population in such a way that the elements within a stratum are as similar as possible and the means of the strata are as different as possible.

Auxiliary information (past or some other information) related to the character under study may be used to divide the popu

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## Question number: 81

» 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

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