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# 6 problems in the theory of statistics, version 8

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**05.07.2013**

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# Description

32 pages

Objective 1

The following information on the work of young turners, randomly selected from the set of 250 young turners working on machine-building enterprises of the city:

Order number Work experience in the company, years Percent Complete production norms,%

1 February 80

1 February 83

96 February 3

3 April 90

2 May 95

98 June 3

....

22 7158

23 7163

24 6125

25 5 150

A statistical analysis of the data. For this purpose:

I. 1) Build a statistical number of workers in the percentage of implementation of development, forming 4 groups with equal intervals. Plot distribution.

2) Calculate the number of characteristics of the distribution of workers by the percentage of implementation of production standards: 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 probability 0.954 determine sampling error average percentage of completion of work norms and boundaries, which will be the average percentage of completion of work norms in the population.

2) determine the error probability of 0.954 share of workers who perform work norms percentage less than 100%, 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 length of service in the company and the percentage of completion of work norms. The results in Table Contents. Draw conclusions.

2) Measure the closeness of correlation between length of service and the percentage of completion of work norms empirical correlations. Explain its meaning.

3) Calculate the parameters of a linear equation the relationship between length of service and the percentage of completion of work norms. 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

The available data on the production of eggs from poultry farms in one area:

Years Egg production, mln. Pieces

1983 56.2

1984 61.2

1985 64.5

1986 65.8

1987 67.8

1988 69.0

1989 71.5

1990 73.4

1991 72.1

1992 70.8

1993 70.6

1994 69.3

1995 65.4

1996 65.8

1997 68.4

Analyze the dynamics of egg production at the poultry farm. To this end:

1) Determine the type of dynamic series.

2) Identify 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) Carry out analytical alignment and express the general trend relevant mathematical equation.

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

6) Assuming that the identification of the trend continue in the future, determine the expected volume of egg production at the poultry farm for the next 5 years. Draw conclusions.

Objective 3

The available data on trade shop "Vegetables":

Quantity of goods sold, kg Price for 1 kg, rbl.

basic accounting basis reporting

Carrots

Beet

Bow 126

64

46390

200

110 2.5

3.0

4.8 2.8

3.8

5.4

Define:

1. Change in the number of items sold and the prices for each product. Specify the type of index used. Draw conclusions;

2. Change in the total turnover of the store as a whole (in% and absolute terms), and also due to: a) changes in the physical volume of trade; b) changes in the price level. Check linking the results to the system. Specify the type of index used. Draw conclusions.

3. Total vo

# Additional information

Task 4

The available data on the return on assets of 2 commercial banks:

Bank Return on Assets (%) The value of assets of banks (mln. Rub.)

basic accounting basis reporting

A

B 1.0

1.8 1.4

2.0 50

120 56

144

Define:

1. Change in return on assets of each bank and the average for banks in the aggregate;

2. The change in the average return on assets due to changes in: a) the actual return on assets of each bank; 6) the proportion of assets held by banks with different levels rentabelnosti.

3. The increase in the total amount of profits earned by banks in the reporting period compared with baseline, as a whole, as well as due to: a) increase the total assets of banks; b) the change in the average level of return on assets; c) changes in the level of return on assets in each bank; d) changes in the share of assets held by banks with different levels of profitability. Check linking the results to the system. Draw conclusions.

Objective 5

Using the equipment for 2 days of the enterprise is characterized by the following data:

Change of the day fit for work machines (pcs.)% Of working for change machines Manufactured parts per hour on one machine (pcs.) Used for changing machine 1 (h)

1 Day 2 Day 1 Day 2 Day 1 Day 2 Day 1 Day 2 Day

First 50 48 80 50 20 25 7.5 7.7

II 44 50 50 60 18 19 7.6 7.8

Third 40 40 40 50 15 17 7.2 7

Build an index factor model changes in the total number of manufactured parts by these factors. Determine the change in the total number of manufactured items (in absolute terms and in%) for Day 2 compared to 1-m in general, and also due to individual factors. Check linking the results to the system. Draw conclusions.

Task 6

Using the data to determine the average for each trait. Formula written using lettering signs. Specify which types of medium used.

Faculty Number of students, people. The number of students in a group, people. Average per session% standouts at the Faculty number of evenings of rest per semester

x y z q p

ESP 25 500 4.2 28 March

GF 250 35 4.3 35 5

BF 200 4.5 30 25 February

MF 750 3.9 28 March 20