# TSU Theory Statistics Option 1 TSU

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CHALLENGE 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. rub.
1 12.8 18.0
2 7.8 12.0
3 4.3 11.9
4 0.8 0.9
5 4.1 5.5
6 8.6 14.6
7 4.3 4.8
8 5.5 5.5
9 4.3 4.8
10 9.1 10.9
11 5.2 9.7
12 4.9 7.2
13 12.7 21.6
14 6.9 7.6
15 5.2 9.7
16 7.3 11.2
17 2.9 4.2
18 4.5 4.9
19 5.3 9.6
20 1.4 3.2
21 7.6 8.6
22 3.6 4.6
23 4.4 6.7
24 6.9 8.4
25 4.6 6.8

A statistical analysis of the data for this purpose:

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

2. Calculate the number of distribution predpriya¬ty characteristics 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 sampling error average profit margins and boundaries, which would be the profit margin in the general population.
2. With a probability of 0.954, determine the error percentage of enterprises whose value of book profit 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 harak¬ter connection between the size of the fixed assets and the amount of profit the company 1. The results are formalized in the table. Draw conclusions.
2. Measure the closeness of correlation between the size of os¬novnyh funds and profit margins korrelyatsion¬nym empirical attitude. 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, poyas¬nite its meaning.
5. Compare the results of the analysis due by analytical groups and regression-correlation method. Draw conclusions.

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. rub.
1983 536
1984 549
1985 567
1986 590
1987 617
1988 625
1989 643
1990 670
1991 684
1992 696
1993 703
1994 725
1995 770
1996 787
1997 792

Analyze the dynamics of the cost of the salable product in the region.

To this end:
1. Determine the kind of dynamic series.
2. Define the analytical parameters of dynamics: absolyut¬ny growth, growth rate and growth (chain and basic) content absolyut¬noe 1% gain. 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 uro¬ven, average annual 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 budu¬schem, determine the expected value of the salable products for the next 5 years.
Draw conclusions.

GOAL 3

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

Products Unit. Meas. Unit cost
production of manufactured products,
thous. units
1st quarter 2nd quarter 1st quarter 2nd quarter
FR-1 pc. 0.9 0.8 500 550
KP-5 m3 1.5 1.4 900 1035

On the basis of these data, determine: