Topic 4 Summarizing and grouping of statistics data

Topic 4 Summarizing and grouping of statistics data 1. The concept and classification of summarizing of statistical data 2. Concepts, tasks and types of statistical groupings

I. Summarizing – is a set of techniques that allow us to obtain summary statistics as summary signs of mass phenomena characterizing the state, relationships and patterns of development of phenomena as a whole The purpose of the summarizing is to collect as a whole the materials of statistical observation and to obtain general statistical indicators that reflect the essence of socio-economic phenomena

In the broadest sense, summarizing is a complex operation of scientific processing of primary statistical data, including secondary control of the collected data, grouping of material, developing a system of indicators for the characterization of typical groups and subgroups, the calculation of totals by groups, and display the grouped materials in the form of analytical tables

Number of operating enterprises by organizational and legal forms of management in agriculture of Ukraine in 2007 Types of enterprises Numbers of enterprises % of total Business associations 7428 12, 7 Private companies 4229 7, 2 Production cooperatives 1262 2, 2 Farms 43475 74, 5 State companies 360 0, 6 Other types of companies 1633 2, 8 Разом 58387 100, 0 TYPOLOGICAL GROUPING

The statistical summarizing consists of the following stages: formulation of goals and objectives of statistical summary formation of groups from observation units, determination of group characteristics, number of groups and interval size; solutions to issues related to the implementation of grouping, highlighting essential features implementation of the technical side of the summary, that is, checking the completeness and quality of the material collected, calculating the results and necessary indicators to characterize the entire population and its part

The statistical summarizing program provides for these types of work the choice of grouping traits establishing the order of formation of groups development of a statistics system to characterize the groups and the entity as a whole development of models of statistical tables for presentation of summary results Choosing of method of summarizing statistical observation data Statistical summarizing of any kind are conducted according to a specific program

Develop a summary program – it means determining which groups and subgroups will be highlighted in the study population, what indicators in the form of summary, average or relative values should be calculated for the selected groups and, in aggregate, in which tables the summarizing results will be drawn up

II. Statistical grouping is the process of creating similar groups in one way or another, based on available statistical data For the proper implementation of statistical grouping, it is important to: a) To make a choice of grouping characteristics; b) determining the number of boundaries of groups and setting the interval in groups; c) the correct assignment of individual units to a particular group.

Depending on the goal and the specific content of the studying material, using groupings solve three main tasks: 1) selection of socio-economic types, categories and other equal groups or statistical populations; 2) study of the internal structure of the phenomena; 3) identification and investigation of causal relationships between the characteristics of the phenomena.

Three types of groupings are used to solve these problems: 1) typological, 2) structural and 3) factorial (analytical). TYPOLOGICAL GROUPING it is a grouping by which the studied set of phenomena distinguishes essentially identical in a significant respect groups, especially classes and socio-economic types. For example, population grouping by social type class composition, enterprises - by type of ownership, products - by economic purpose, etc. STRUCTURAL GROUPINGS solve the second problem of groups - reveal the internal structure of phenomena. They give information about which parts of the set of phenomena under study, what structure of types of phenomena and what indicators characterize the individual parts FACTORIAL GROUPINGS make connections between factorial and resultant attributes. They are based on the study of how in the mass phenomena with the change of one or more factor traits changes the productive attribute

Population grouping of Ukraine by gender in 2007 (01/01/2008) Gender Population Millions of people % of total Men 21, 3 46, 1 Women 24, 9 53, 9 Total 46, 2 100, 0 STRUCTURAL GROUPING

Dependence of grain yield on its factors in the forest-steppe zone of the region Groups of farms by yield, quintals / hectare Mineral fertilizers There average per hectare of annual workers Soil quality, points cereals , quintals per 100 hectares of of active arable land, substance ) people. Number of farms Average yield, quintals / hectare I – less than 25, 0 16 22, 1 52, 0 1, 41 15, 6 II - 25, 1 - 30, 0 21 27, 7 58, 2 1, 64 17, 4 III - 30, 1 - 35, 0 38 32, 6 69, 4 2, 12 17, 5 IV – more than 35, 0 15 38, 4 81, 0 2, 75 19, 3 On the average 90 31, 5 67, 7 2, 07 17, 3 FACTORIAL GROUPING

Grouping is carried out in three stages: 1 The choice of grouping signs by which grouping will be carried out 2 selection of groups (intervals) by group characteristics 3 direct grouping of material and characterization of separated groups and subgroups by statistical indicators

The number of intervals depends on the variation of the grouping attribute: the larger its fluctuations, the more groups should be formed. The number of intervals should take into account the number of units of the population. Open intervals are called those with only one boundary, upper or lower; The upper and lower limits are indicated in closed intervals. The intervals may vary in size. The magnitudes of the open intervals are uncertain, and the magnitudes of the closed intervals are set as the differences between the upper and lower bounds of their adjacent groups. Closed intervals are divided into equal and irregular.

Equal intervals are called those in which the differences between the respective (upper or lower) boundaries of the intervals are the same. At irregular intervals, the differences are not the same. Irregular intervals are usually increasing. Of particular importance are the multiple intervals with different growth rates. If the growth factor is 2, then each successive interval is greater than the previous two times.

Example. 1. If the number of workers in the enterprises of the industry varies from 50 to 3150 people, the scale of intervals by the number of workers can be submitted as follows: 50 - 150 - 350 - 750 – 1550 - 3150 These are closed irregular multiples intervals with a growth rate of 2: the first interval here is 100 (150 - 50), the second is 200 (350 - 150), the third is 400, the fourth is 800, the fifth is 1600.

The interval is determined by the formula – is the interval; xmax and xmin are the maximum and minimum values of the characteristic; n is the number of defined intervals

Example 2. Task. The maximum length of work experience is 45 years, the minimum is 5 years, and it is decided to form five equal intervals. To calculate the value of the equal interval. Solution: The value of the equal interval is: = (45 - 5) / 5 = 8.

The Sturgess formula can be used to calculate the magnitude of equal intervals: N is the number of units of the population

Example 3. Task. Thus, if the maximum length of work experience is 45 years, the minimum is 5 years, and it is decided to form equal intervals, and the number of units of the population is 100. Solution: The value of the equal interval is: = (45 - 5) / 1+5, 322. = 6, 327.

Task 1. Required: According to table 1 to build a discrete and combinational series of distribution over the shelf life and the point of reducing the quality of cheese, forming on this basis the following groups: from 0 to 1 point; 2 - 3 points; 4 - 6 points. To determine the dependence of the quality of the cheese on the shelf life to carry out analytical grouping. Draw conclusions. DATA: Table 3. 2. Data on shelf life and quality reduction of 20 batches of Ukrainian cheese Batch № Shelf life , month. Quality reduction , Batch № Shelf life , month. points Quality reduction , points 1 2 3 4 5 6 1 2 2 11 3 4 2 4 4 12 4 2 3 3 4 13 3 4 4 3 3 14 1 0 5 3 5 15 4 6 6 2 2 16 2 1 7 2 1 17 3 2 8 2 3 18 1 1 9 4 3 19 3 3 10 4 5 20 1 0

Batches grouping by shelf life of cheese Shelf life , month. Number of batches % of total 1 2 3 4 Total Combinational distribution of cheese batches by shelf life and quality reduction Shelf life , month. 1 2 3 4 Total Quality reduction , points 0– 1 2– 3 4– 6 Total

Аналітичне групування партій Shelf life , month. 1 Total in a group 1 2 Total in a group 2 3 Total in a group 3 4 Total in a group 4 Total by population Number of batches Quality reduction , points

Determination of the average score for reducing the quality of cheese Shelf life , month. 1 2 3 4 Total Number of batches Total, points Average point

Task 2. Required: To build a discrete variation series of the distribution of young workers by skill level. To make a conclusions about elements of the distribution row. DATA: Table 3. 3. Skill levels of young workers, graduates of vocational schools 5 4 4 5 3 4 3 4 5 3 4 4 4 5 4 4 3 4 5 5 3 4 4 4

Task 3. Required: To construct an interval variation series of customer distribution over the duration of one purchase, forming 4 groups with the same intervals. Performance data: During a sample check of 30 shoppers, it was determined that the duration of one purchase in the confectionery department of the shop was (table 3. 5): DATA: Table 3. 5. Duration of one purchase in the confectionery department, seconds 77 70 82 81 81 82 75 80 71 80 81 89 75 67 78 73 76 78 83 76 82 69 61 66 84 72 74 82 82 76

Task 4. Required: According to the table 3. 64: Carry out a combined distribution of drivers by class and monthly earnings, to build ranks of distribution of drivers by class, monthly earnings, forming 4 groups at the same intervals. Performance data: DATA: Table 3. 6. Monthly earnings and class of 20 drivers Monthly earnings, Number of driver Class of driver Monthly earnings, dollars Number of driver Class of driver 1 II 1750 11 I 2870 2 I 2900 12 II 1800 3 II 1700 13 II 1700 4 II 1760 14 I 2930 5 II 1800 15 II 1750 6 II 1750 16 II 1750 7 II 1820 17 I 2950 8 II 1730 18 I 2890 9 II 1750 19 II 1800 10 II 1780 20 I 2900 dollars

Task 5. Required: According to table 3. 7, to group the regions by population. To justify the required number of groups on this basis. For each group of regions, set the number of regions, population, income together and on average per area, services received by the population - together and on average per inhabitant. Group the results as a spreadsheet. To make a conclusions. Table 3. 7. Population data, income and volume of services received by the population in the regions of Ukraine Region Population Income, millions Services, received by the population in of hryvnias regions, millions of hryvnias Вінницька 1 631 302 30592 Волинська 1 039 988 17012 647, 6 Дніпропетровська 3 312 963 78963 3763, 3 Донецька 4 389 056 108786 3661, 8 Житомирська 1 270 897 23517 675, 6 Закарпатська 1 252 126 18314 618, 5 Запорізька 1 787 110 41576 1831, 4 Івано-Франківська 1 380 673 23789 769, 4 Київська 1 721 947 38511 1453, 1 м. Київ 2 814 043 117367 24638, 2 999 397 46984 654, 6 Луганська 2 264 493 48924 1295, 3 Львівська 2 539 041 23188 2926, 7 Миколаївська 1 175 721 45091 815, 7 Одеська 2 387 349 30369 3793, 9 Полтавська 1 472 798 19654 960, 8 Рівненська 1 155 314 22098 604, 3 Сумська 1 148 215 17329 787, 8 Тернопільська 1 078 944 58878 502, 4 Харківська 2 732 935 18687 3371, 3 Херсонська 1 081 456 24334 726, 5 Хмельницька 1 318 141 22805 658, 5 Черкаська 1 274 391 14146 905, 0 Чернівецька 904 975 20462 539, 8 Чернігівська 1 084 211 2537 634, 6 Кіровоградська 966, 1