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# Examination - Theory of Statistics TSU 1 option

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**17.08.2012**

Content: 20817161650820.doc (493 kB)

# Description

A total of 6 tasks

Objective 1

As a result, 10% of the survey sample (random repetition-free selection) of privatized enterprises of the industry following results were obtained:

Number Enterprise Cost industrial fixed assets (annual average), mln. Rub. The balance sheet profit, mln.

1 12.8 18.0

2. 7.8 12.0

3. 4.3 11.9

4. 0.8 0.9

A statistical analysis of the data for this purpose:

I. 1. Build the statistical distribution of a number of companies in terms of profit, forming 4 groups with equal intervals. Plot number distribution.

2. Calculate the characteristics of a number of distribution companies in terms of profit: the arithmetic mean, the average linear deviation, variance, coefficient of variation. In calculating the arithmetic mean and standard deviation using the method of moments. Draw conclusions.

II.

1. With a probability of 0.954, determine the average size of sampling error of profit and the border, which will be the profit margin in the general population.

2. With a probability of 0.954, determine the error percentage of enterprises whose production volume does not exceed 5.0 mln. Rub., And the border, which will be the proportion in the population. Draw conclusions.

III.

1. The method of analysis groups set the nature of the relationship between the size of the fixed assets and the amount of profit per 1 plant. The results are formalized in the table. Draw conclusions.

2. Measure the closeness of correlation between the size of the fixed assets and profit margins empirical correlations. Explain its meaning.

3. Calculate the parameters of a linear equation of the relationship between the size of the fixed assets and profit margins. Explain the meaning of the regression coefficient.

4. Calculate the theoretical correlation ratio, explain its meaning.

5. Compare the results of the analysis due by analytical groups and regression-correlation method. Draw conclusions.

Task 2

Change in the value of commodity products produced by industrial enterprises of the region in comparable prices is characterized by the following data:

Years Cost of commodity output in comparable prices, bln. Rubles.

1983 536

1984 549

Analyze the dynamics of the cost of the salable product in the region. To this end:

1. Determine the kind of dynamic series.

2. Determine the analytical performance indicators: absolute growth, growth rate and growth (chain and basic), the absolute content of 1% growth. The calculation results are complete your table. Show the relationship of chain and benchmarks.

3. Determine the dynamic average for the period: the average number of annual average growth rate and growth.

4. To determine the general trend of commodity production make analytic alignment and express the general trend relevant mathematical equation.

5. Determine aligned (theoretical) levels of a number of speakers, and apply them on the chart with the actual data.

6. Assuming that the identified trend will continue in the future, determine the expected value of the salable products for the next 5 years. Draw conclusions.

Objective 3

Cost and volume of production plant "Vanguard" for the two adjacent quarter is characterized by the following data:

Products unit cost of manufactured products,

thous. units

1st quarter 2nd quarter 1st quarter 2nd quarter

FR-1 pc. 0.9 0.8 500 550

KP-M3 5 1.5 1.4 900 1035

On the basis of these data, determine:

1. Changes in the cost and volume of product produced for each product (in%). Specify the type of index used.

2. Changes in the cost of production of all products in the 2nd quarter compared with the 1st quarter as a whole (in% and absolute terms), as well as by changing the number of products and unit cost of the product. Show the relationship of calculated indices and absolute amounts. Specify the type of use of the index.

3. The general index of unit cost and the number of products