А нужно ли эти законы изучать, не мешает ли это творчеству, основанному, как известно, на вдохновении?

 

5.1. The following data represent the provision of living quarter:

Classes of people by living quarter per person, m2	Up to 10	10-12	12-14	14-16	16-18	18-20	More than 20
Number of people, %

Find:

1) Average living quarter per person;

2) The standard deviation; the variance, the rate of variation, the quartiles, the coefficients of skewness and kurtosis. Draw conclusions.

 

 

 

5.2. There is the following data about wage:

Wage, thousand rubles	Up to 3	3-5	5-7	7-9	9-11	More than 11
Number of workers, people

Find:

1) Average wage;

2) The standard deviation; the variance, the rate of variation, the quartiles, the coefficients of skewness and kurtosis. Draw conclusions.

5.3. The following data represent how the plan has been executed by the group of workers:

Classes of workers by rate of execution of plan, %	Rate of execution of plan, %
Up to 100	90, 95, 85, 92
100 and more	100, 102, 104, 103, 105, 104

Find: the within-group variance, the external variance and the population variance, using the sum rule of variances.

 

5.4. The distribution of population by the salary is characterized by the following data:

Scope	Average wage, thousand rubles	Number of people	The standard deviation, thousand rubles
Medical services
Educational services

Find: the within-group variance, the external variance and the population variance, population standard deviation and rate of variation, using the sum rule of variances.

5.5. The following data represent the deposits of urban and rural population:

Classes of population	Number of depositors, thousand people	Average deposit, thousand rubles	Within-group coefficient of variation, %
Urban population
Rural population

Find: the within-group variance, the external variance and the population variance, population standard deviation and rate of variation, using the sum rule of variances.

 

Student_________________________

Group_______________________

Moscow

CONTENT

 

Chapter 2. Frequency distribution and graphs. 3

Chapter 3.Relative Ratio.. 8

Chapter 4. Measures of central tendency.. 13

Chapter 5. Measures of dispersion.. 22

Chapter 2. Observation and organizing data.

2.1. The following data represent the activity of banks, million rubles

#	Total assets	Owned capital	Debt capital	Balance profit
	645,6	12,0	27,1	8,1
	636,9	70,4	56,3	9,5
	629,0	41,0	95,7	38,4
	619,6	120,8	44,8	38,4
	616,4	49,4	108,7	13,4
	614,4	50,3	108,1	30,1
	608,6	70,0	76,1	37,8
	601,1	52,4	26,3	41,1
	600,2	42,0	46,0	9,3
	600,0	27,3	24,4	39,3
	592,9	72,0	65,5	8,6
	591,7	22,4	76,0	40,5
	585,5	39,3	106,9	45,3
	578,6	70,0	89,5	8,4
	577,5	22,9	84,0	12,8
	553,7	119,3	89,4	44,7
	543,6	49,6	93,8	8,8
	542,0	88,6	26,7	32,2
	517,0	43,7	108,1	20,3
	516,7	90,5	25,2	12,2

Construct frequency distribution using grouping of banks by owned capital, using formula by Sturges. Add the variables, enabling to construct the analytical grouping. Display graphs and table, and draw conclusions.

2.2. Using the data of 2.1, construct the frequency distribution using grouping of banks by balance profit, formed 4 groups, characterizing the structure of banks. Display pie graph.

2.3. Using the data of 2.1, construct frequency distribution using the analytical grouping, sorted out the influencing and resulting variables. Use table and graph forms for displaying data.

2.4. The following data represent the experience of workers:

Classes of worker by experience, years	Number of workers, %	Production output, %
3-5
5-6
6-8
8-10
10-15
15-18
18-20
20-25
Total:

Applying the secondary grouping, construct the grouping of workers by experience, using the following classes: 3-5, 5-10, 10-15, 15-20, 20-25. Calculate the both variable for each group.

2.5. The following data represent the wage:

Classes of workers by wage, dollars	Number of workers, unit	Wage fund, dollars
300-400
400-500
500-600
600-700
700-800
800-900
900-1000
1000-1100

Applying the secondary grouping, construct the grouping, using 5 groups. Calculate the both variables for each class.

2.6. The following data represent the non-current assets of enterprises, billion rubles:

Classes of enterprises by non-current assets, billion rubles	Number of enterprises, %	Production output, %
1-3	4.6	0.6
3-5	13.6	6.2
5-10	15.9	9.9
10-30	52.3	59.4
30-50	13.6	23.9
Total:	100.0	100.0

Applying the secondary grouping, construct the grouping of enterprises by non-current assets, using the following classes: 1-3, 3-5, 5-10, 10-15, 15-20, 20-30, 30-50. Draw conclusions and calculate the both variables for each class.

 

Chapter 3.Ratio s

3.1. The production of oil and coal are characterized by the following data:

Fuel	Production, million tons
April	May	June
Oil	23,8	25,0	24,2
Coal	23,2	20,2	18,7

Combustion heat of oil is 45,0 мilliJoule/kg, coal – 26,8 мilliJoule/kg. Find then production of fuel for the 2^d quarter using the standard unit of the equivalent oil by the combustion of heat is 29.3 мilliJoule/kg. Compare the production of fuel for each month.

3.2. The production output is characterized by the following data: notebook of 96 sheets – 15 thousand units; 48 sheets – 30 thousand units, 18 sheets – 45 thousand units, 12 sheets – 90 thousand units. Find the total production volume of standard unit is 12 sheets.

3.3. The following data represent balance sheet profit of two companies:

Company	Balance sheet profit in 2001, thousand doll.	Balance sheet profit in 2002
planned	current
А
B
Total:

Find all ratios.

3.4. The following data represent the production of paper:

Production volume, thousand tons

Find ratios of time and set the correlation between them.

3.5. The following data represent the production volume of productive industries:

Productive industry	Hungary	Germany	Russia
Electric-power industry, bill. kwatt*h
Artificial resin, mill. ton.	0,7	10,5	1,5
Saw-timber, mill. m3	0,6	14,1	32,1

Find the ratios of intensity, using the following data about population (million people): Hungary – 10,3; Germany – 81,4; Russia – 142,3.

3.6. The following data represent total expenses of a company:

Expenses	Proportion, %
Raw materials
Fuel
Wage fund
Depriciation
Other expenses
Total:

Find ratios of co-ordination.

3.7. The population is characterized by the following data:

	Previous year	Reporting year
Population, thousand people	139,0	147,9
Employees of a government-financed organization, thousand people	14,6	18,8
including
doctors	6,2	8,4
teachers	5,7	7,7
librarians	1,5	1,4
museologists	1,2	1,3

Find ratios if intensity, structure and co-ordination.

3.8. Using ratio of comparison, compare the volume of securities:

Bank	Volume of securities, million units
State Street Bank
Euroclear
Citibank
Chase Manhattan
Barclays
Midland

 

Chapter 4. Measures of central tendency

4.1. The following data represent the repayment period of banks:

Repayment period, months	1-2	2-3	3-4	4-5	5-6	6-7	More than 7
Number of banks, %

Find: the average repayment period, mode and median.

4.2. Find average bond:

	Bond, rubles
Issued, million units

4.3. The following data represent wage of bank staff.

Classes of staff by wage, dollars	Number of staff, %
500-600
600-700
700-800
800-900
900-1000
1000-1100
More than 1100
Total:

Find the average wage, mode and median. Draw conclusions.

4.4. The production output is characterized by the following data:

Company	Planned	Fact
Proportion of extra-class output, %	Value of extra, thousand dollars	Proportion of extra-class output, %	Value of production output, thousand dollars

Find average proportion of extra-class output for two companies: 1) planned; 2) fact.

4.5. The following data represent the lending operations of banks:

Bank	Short-term credit	Long-term creditит
Average interest rate, %	Amount of credit, million rubles	Average interest rate, %	Revenue, million rubles

Find average interest rate for two banks.

4.6. The following data represent the production output of three plants:

Plant	Production output in the 2d quarter, thousand rubles	Execution of plan, %	Proportion of extra-class output, %
	1040.0	103.2	96.1
	890.0	107.6	84.3
	670.5	97.2	75.6

Find a) average execution of plan for all plants; b) average proportion of extra-class output for all plants. Draw conclusions and explain the equations have been used.

4.7. The following data represent the cargo transportations:

Type	1st quarter	2nd quarter
Distance, km	Total freight turnover, tons*km	Distance, km	Total volume of freight, tons
Electric locomotive				7.0
Diesel locomotive				9.0

Find average length of haul: а) for the 1^st quarter; b) for the 2^nd quarter; c) for the 1^st halfyear.

4.8. The following data represent the production volume of three factories:

#	Previous year	Reporting year
Total volume of production output,	Labor output rate per unit, hours	Total labor inputs, hours	Labor output rate per unit, hours
	52.0	0.34		0.35
	46.0	0.50		0.46
	24.0	0.46		0.46

Find the average labor output rate per unit for three factories: а) in the previous year; b) in the current year. Compare results and draw conclusions.

4.9. The following data represent the execution of plan by workers:

Execution of plan, %	Up to 100	100-110	110-120	120-130	130-140	More than 140
Number of workers

Find average execution of plan by workers, mode and median.

4.10. Dividend yield for each year equals of 8, 10 and 12% annual. Find average dividend yield.

4.11. The Insurance company proposes to buy the insurance policy for 5 years with annual income of 5, 7, 9, 12, 15%. Find average interest rate of income.

 

4.12. The following data represent the distribution of enterprises by turnover:

Classes of enterprises by turnover, million rubles	Number of enterprises, %
700-800
800-900
900-1000
1000-1100
1100-1200
1200-1300
More than 1300
Total:

Find the average turnover (using mathematical properties of the mean), mode and median. Present results in table and graph forms. Set the mode and the median, using the graphical forms. Draw conclusions.

4.13. The following data represent the wage fund, wage and workers of two branches:

#	Wage fund, dollars	Number of workers, units	Average wage, dollars	Proportion of workers, %
А

Find average wage of workers, using the following columns: а). 1 and 2; b). 2 and 3; c). 1 and 3; d). 3 and 4.

4.14. The following data represent the production value per one worker:

Classes of enterprises by the production value per one worker, thousand rubles	Number of workers, units.
800-1000
1000-1200
1200-1400
1400-1600
1600-1800
1800-2000
Total:

Find the average production value per one worker (using mathematical properties of the mean), mode and median. Presents the results in table and graph forms. Set the mode and the median, using the graphical forms. Draw conclusions.

Chapter 5. Measures of dispersion

5.1. Below is the data about the noncurrent assets:

Classes of enterprises by non-current assets, million USD	Number of enterprises, units	The noncurrent assets per one enterprise, million USD	Within-group variances
1.2-2.7		1.8	0.17
2.7-4.2		3.2	0.09
4.2-5.7		4.8	0.25
5.7-7.2		6.9	0.14

Find: the within-group variance, the external variance and the variance, using the sum rule of variances; the standard deviation, the rate of variation, the quartiles.

5.2. The following data represent the distribution of depositors by the amount of deposit:

Amount of deposit, thousand dollars	Up to 4	4-6	6-8	8-10	More than 10
Number of depositors

Find:

1) Average amount of deposit;

2) Variance, standard deviation, rate of variation;

3) Quartiles and deciles.

5.3. The distribution of workers by the production volume is characterized by the following data:

Production volume per one worker, thousand rubles	Up to 10	10-11	11-12	12-13	13-14	More than 14
Number of workers, people

Find:

1) Average production volume per worker;

2) The standard deviation; the variance, the rate of variation, the quartiles, the coefficients of skewness and kurtosis. Draw conclusions.

5.4. The following data represent the results of survey of 100 families:

Classes of families by average income per person, thousand USD	Number of families, units	Classes of families by average income per person, USD	Number of families, units
Up to 0.1		0.25-0.3
0.1-0.15		0.3-0.35
0.15-0.2		More than 0.35
0.2-0.25		Total:

Find the variance, the standard deviation, rate of variation, quartiles and skewness and kurtosis coefficients. Draw conclusions.

5.5. The following data represent the distribution of branches of enterprises

Classes of enterprises by the production value, million rubles	Number of branches of each enterprise, units
А
Up to 3
3-6
6-9
9-12
12-15
15 and more
Total:

Find different types of the variance, using the sum rule of variances, population standard deviation, population rate of variation. Draw conclusions.

 

 

 

А нужно ли эти законы изучать, не мешает ли это творчеству, основанному, как известно, на вдохновении?

Нужно. Профессиональный художник отличается от пусть даже талантливого любителя и дилетанта тем, что знает, как надо работать.

О сценаристе и режиссере, не владеющим основными законами построения сценария, можно сказать словами шекспировского персонажа Ипполита из комедии «Сон в летнюю ночь»: «Он сыграл свой пролог, как ребенок играет на флейте: звук есть, но управлять им он не умеет».

«Творить, не осознавая законов своего искусства, попросту невозможно» (А. Тарковский).

Знание законов — это и необходимое условие их преодоления и прорыва к творческой свободе…

Существует сомнение: а есть ли в реальности такая наука — «теория кинодраматургии? Сомнение произрастает на почве рассуждений о том, что среди теоретических воззрений на построение сценария и фильма мы находим целый ряд взглядов и направлений, в большей степени отличающихся, а порой прямо противоречащих друг другу.

Но разве существование различных направлений служило когда-либо достаточным основанием для отрицания научности той или иной дисциплины? Литературоведение, психология, не говоря уже о философии… Сколько в них систем взглядов, школ, которые, казалось бы, начисто опровергают друг друга. «Было пять или пять тысяч философов, которые объясняли вселенную совершенно по-разному» [1]. Но в каждом из направлений, если оно было достаточно серьезным, содержались зерна истины, из которых вырастало общее древо научного знания.

И потом: что есть закон в искусстве, в том числе и в кино? Он ведь — квинтэссенция практического опыта отдельных личностей и целых поколений художников; опыта, который затем оформился как необходимость.

В истории кино бывали случаи, когда теория обгоняла практику, открывала ей пути. Так, методы истинно кинематографического использования звука в кино, соотнесения его с изображением были открыты чисто теоретически до их воплощения на экране. Они были опубликованы в 1928 г. в известной «заявке» С. Эйзенштейна, В. Пудовкина и Г. Александрова, которая называлась: «Будущее звуковой фильмы».

Но, конечно же, значительно чаще практика в искусстве идет впереди теории. Теория эти творческие открытия обобщает.

Однако существуют ли в кино особые, присущие только ему законы построения сценария и фильма, отличающиеся, скажем, от законов построения романа или пьесы? Конечно, существуют. Они основаны на специфике кино как вида искусства.