# ISS (Statistical Services) Statistics Paper III: Questions 57 - 62 of 109

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## Question number: 57

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2012

### Write in Short

Show that mean of a systematic sample is more precise than the mean of a simple random sample of size n under a certain condition to be obtained by you.

## Question number: 58

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

Appeared in Year: 2013

### Describe in Detail

Discuss Engel’s curve. Explain the Engel’s curve for constant price of a demand function where is national income and p is price.

### Explanation

**Engel’s curve:** The graphic representation of the basic relationship between household income and its expenditure on a particular item of consumption is known as Engel’s curve. The Engel curves shows the effect of a change in income on the expenditure for each good at fixed prices. If price change, the result will be shift in each of the Engel curve

… (321 more words) …

## Question number: 59

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

Appeared in Year: 2012

### Describe in Detail

What are the different methods for measurement of trend? Discuss the method of fitting a straight line using least squares method.

### Explanation

**Methods of measurement of trend:**

Trend can be measured by the following methods:

(i) Graphic method or trend by Inspection

(ii) Method of Semi-Averages

(iii) Method of Curve fitting by principles of Least Squares

(iv) Method of moving averages

**Fitting a straight line using least squares method:**

Let be the trend equation.

Where = compute

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## Question number: 60

» 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 with reference to the base year

= Total of the p

… (311 more words) …

## Question number: 61

» 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,

… (307 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.