Bar chart analysis. Bar charts. Construction of a cumulative curve

15.02.2022

4. Classification and rules for constructing statistical graphs.

Statistical graphs are distinguished by the content and method of construction.

According to the method of construction, they distinguish:

columnar

tape

linear

square

circular

pie charts

When building columnar diagrams, a rectangular coordinate system is used. In this case, each value of the studied indicator is displayed as a vertical column. The base of the columns is placed along the abscissa axis. Their width can be arbitrary, but must be the same for each column. The height of the columns (according to the scale adopted along the y-axis) must strictly correspond to the displayed data.

The number of columns is determined by the number of indications (data) studied. The distance between the columns should be the same. At the base of the columns, the name of the indicator under study is given.

Varieties of bar charts make up the so-called tape diagrams.In these diagrams, the bases of the columns are placed vertically, and the scale scale is applied to the horizontal axis. In its form, a strip chart represents a series of strips of the same width extending along the abscissa. The length of the stripes (ribbons) corresponds to the values of the displayed indicators. When constructing strip charts, the same requirements are observed as when constructing bar graphs (the same width of the bars, the beginning of the scale from zero, etc.).

For building linear graphs use a system of rectangular coordinates. Usually, time (years, months) is plotted along the abscissa axis, and the sizes of the depicted phenomena or processes are plotted along the ordinate axis. Scales are applied on the y-axis. Particular attention should be paid to their choice, since the general appearance of the graph depends on this. Ensuring balance, proportionality between the axes of coordinates is necessary in the schedule due to the fact that the imbalance between the axes of coordinates gives an incorrect image of the development of the phenomenon.

Often, several curves are shown on one line graph, which give a comparative description of the dynamics of various indicators or the same indicator.

However, more than three or four curves should not be placed on one graph, since a large number of them inevitably complicate the drawing and the line diagram loses its clarity.

For a simple comparison of indicators that are independent of each other, diagrams can be used, the construction principle of which is that the compared quantities are depicted in the form of regular geometric figures, which are constructed so that their areas are related to each other as the quantities depicted by these figures. In other words, these diagrams express the magnitude of the phenomenon depicted by the size of their area.

To obtain diagrams of the type in question, a variety of geometric shapes are used - square, circle. It is known that the area of a square is equal to the square of its side, and the area of a circle is determined in proportion to the square of its radius. Therefore, to build diagrams, you must first extract the square root from the compared values. Then, based on the results obtained, determine the side of the square or the radius of the circle, according to the accepted scale.

are widely used in statistics. pie charts. In these diagrams, the area of the circle is taken as the value of the entire statistical population under study, and the areas of individual sectors display the specific gravity (share) of its constituent parts. That is, the area of the circle in it is taken as 100%, and the sizes of the sectors are proportional to the ratio of the constituent parts of the whole in their total. The structure is depicted as a percentage, with one percent equal to 3.6 degrees.

comparison graphs

dynamics graphs

structure charts

plan execution schedules

variation series charts

charts of interrelated indicators

When plotting charts, you must adhere to the following rules:

Each graph should have a title that is placed below it. The title should briefly reflect the content, place and time of the phenomenon.

All graphs in the text are consecutively numbered and referred to as a “figure”.

Coordinate axes must be named and have units.

On the y-axis and on the numerical axis, figures should be plotted on an equal scale. The numerical axis should end with a value that is slightly greater than the maximum value in the original population.

Under the figure (where necessary), explanations of the conditional images used on the chart should be given.

In the text part of the work, the graph should be placed after the reference to it in the text on the same page or on the next.

Each graph in the text part of the work should be commented.

Let's consider on specific examples each type of graphs and the corresponding methods of graphical representation of statistical data.

5. Examples of the practical use of graphs.

5.1 Comparison graphs.

Comparison diagram - shows the ratio of the sign of the statistical population. When constructing comparison graphs, bar (Fig. 1), strip (Fig. 2), square (Fig. 3) and circular (Fig. 4) charts can be used.

As an example of a bar chart, let's take data on commercial products of various enterprises for the reporting period: enterprise No. 1 - 103099 million rubles, enterprise No. 2 - 122282 million rubles, enterprise No. 3 - 89329 million rubles, enterprise No. 4 - 88716 million rubles

As can be seen from the graph, the largest amount of marketable products falls on the share of enterprise No. 2, a little less on enterprise No. 1, and the smallest number - on enterprises No. 3 and No. 4, in which the number of marketable products is approximately equal.

To build a ribbon chart, we take the following data: change in costs by 1 rub. marketable products at the enterprise for the reporting year (in % of the previous year) are characterized by the following values: enterprise No. 1 - (+0.26%), enterprise No. 2 - (-0.74%), enterprise No. 3 - (-0, 79%), enterprise No. 4 - (-0.24%), enterprise No. 5 - (-0.5%).

After analyzing the schedule, we can say that only at enterprise No. 1, the costs of 1 rub. marketable products increased (by 0.26%), while the rest decreased, with the largest decrease occurring at enterprise No. 3 (-0.79%).

It is advisable to build a square and a pie chart in the case when the difference between the compared indicators is so large that it becomes difficult to establish a suitable scale. To find the side of the square, as mentioned earlier, find the square root of the corresponding value. Then the area of the squares will visually characterize the corresponding initial value.

Consider the following data: the output of certain types of products of the enterprise is characterized by the following data: product No. 1 - 4225 million rubles, product No. 2 - 2500 million rubles, product No. 3 - 625 million rubles. Then the sides of the squares will be: No. 1 - √4225 = 65, No. 2 - √2500 = 50, No. 3 - √625 = 25. Set the scale: 1 cm = 25 million rubles. Then we get the following diagram.

As can be seen from the diagram, product #1 produced the largest amount, product #2 - less, and product #3 produced the least amount.

To build a pie chart, let's take the data from the previous example. To find the radius, we take the square root of the corresponding values, then we have the following diagram:

And, judging by the diagram, the largest number of products #1 was produced, then products #2, and the least number of products #3 was produced.

5.2. Dynamic charts.

Diagram of dynamics - shows the change of the phenomenon in time. The construction of dynamics graphs is carried out, as a rule, using linear (Fig. 5, Fig. 5.1.) or bar (Fig. 6) diagrams.

To build a linear diagram of the dynamics, we take the following data: the growth rate of production at enterprise No. 1 (in% compared to December of the previous year) was: January - 104%, February - 101%, March - 107.3%, April - 111.3% , May - 115%.

Under these conditions, it is recommended to build a scale without a vertical zero, i.e., the scale of values breaks close to the zero line and only a part of the entire possible field of the graph falls on the diagram. This does not lead to distortions in the image of the dynamics of the phenomenon, and the process of its change is drawn more clearly by the diagram.

It can be concluded that during the period under review there is a monthly increase in output, with the most significant increase in output in May (by 15%), while in February the increase was insignificant (1%).

For an example of displaying several indicators on a line chart, we add to the previous data the indicators of enterprise No. 2, the growth rate of production at which (in% compared to December of the previous year) was: January - 109%, February - 111%, March - 114.3%, April - 119.3%, May - 125%.

As can be seen from this graph, for the period under review, there is a monthly increase in output at both enterprises, and both enterprises reached the maximum increase in output in May, and the least increase in output was at enterprise No. 1 in February, and at enterprise No. 2 - in January . However, in general, the most significant increase in output was at enterprise No. 2.

As an example of a bar graph, let's take the data on the harvest of sugar beet: in 2002 it was 15.7 million tons, in 2003 - 19.4 million tons, in 2004 - 21.8 million tons, in 2005 - 21.4 million tons and in 2006 - 30.9 million .tons

As can be seen from the graph, the least amount of sugar beet for this period was harvested in 2002 (15.7 million tons), while the largest harvest was in 2006 (30.9 million tons). In general, sugar beet harvests have increased every year, with the exception of a slight decline in 2005.

5.3. Structure charts.

Structural diagram - allows you to compare statistical populations by composition. When constructing graphs of the structure, sector (Fig. 7) and bar (Fig. 8) charts can be used.

The area of a circle in a pie chart is taken as 100%, and the size of the sectors is proportional to the percentage of the constituent parts of the whole in their total.

Let's take the following data: workers of 6 wage categories work in the shop, the number of workers of the 1st category in the total number of workers is 1.5%, 2nd category - 6.1%, 3rd category - 32%, 4th category - 34.5%, 5th category - 17.3% and 6th category - 8.6%.

As can be seen from the sector diagram, the smallest share in the total number of workers in the workshop is made up of workers of the 1st category - 1.5%, then, in ascending order, there are workers of the 2nd and 6th categories, which make up approximately equal shares, 6.1% and 8.6%, respectively, followed by the 5th category - 17.3% and the most numerous are workers of 3 and 4 categories, which account for 32% and 34.5%, respectively.

To depict the structure graph using a bar chart, consider the structure of people employed in the economy by type of economic activity. Agriculture (1) employs 10.8%, mining, manufacturing, production and distribution of electricity, gas and water (2) - 21.3%, construction (3) - 7.6%, wholesale and retail trade (4 ) - 18.6%, transport and communications (5) - 8.1%, public administration, compulsory social security (6) - 6.6%, education and health (7) - 15.8%, other activities (8) - 11.2%. Let's build a diagram.

As can be seen, most people are employed in category 2 - mining, production and distribution of electricity, gas and water (21.3%), as well as in category 4 - wholesale and retail trade (18.6%). Next comes the 7th category - education and healthcare (15.8%). Then follow the 8th and 1st categories - these are respectively other types of activity (11.2%) and agriculture (10.8%). And the smallest share of the employed falls on categories 5, 3 and 6 - these are transport and communications, construction and public administration, compulsory social security, respectively, the share of each of these categories does not exceed 9% of the total number of employees.

5.4. Plan implementation schedules.

Plan performance indicators can be displayed graphically in the form of a linear (Fig. 9) and bar (Fig. 10) charts.

To build a line diagram, we take the following data: the implementation of the plan for the production of marketable products by the shop is characterized by the following data: January - 108%, February - 110%, March - 104%, April - 108%, May - 112%.

According to the schedule, the following conclusion can be drawn: a higher percentage of overfulfillment of the plan falls on February of the reporting period - 110%, while in March it amounted to a minimum value - 104%.

The fulfillment of the plan for the production of marketable products by the workshop is characterized by the following data: I quarter - 110%, II quarter - 107%, III quarter - 109%, IV quarter - 108%, based on these data, we will build a bar chart of the plan.

It can be seen from the graph that the highest percentage of overfulfillment of the plan falls on the 1st quarter - 110%, while this indicator was the lowest in the 2nd quarter, when it amounted to 107%.

5.5. Graphs of variational series.

Among the variational distribution series, discrete (when individual options have certain specific values) and interval (when options fluctuate within certain limits) series are distinguished. Discrete variation series are depicted as a so-called distribution polygon (Fig. 11). Options are plotted on the abscissa axis, frequencies - on the ordinate axis. The points of intersection are connected by line segments.

Let's take data on the distribution of workers at the enterprise according to their tariff categories: 1st category - 10 people, 2nd category - 15, 3 - 22, 4 - 109, 5 - 96 and 6th category - 32 people.

As can be seen from the graph, the largest number are workers of 4 and 5 categories - 109 and 96 people, respectively, while the number of workers of 6, 3 and 2 categories does not differ much from each other and fluctuates around 15 - 30 people, and the smallest group make up a worker of the 1st category - 10 people.

Interval variation series are depicted as a histogram (Fig. 12). When constructing a histogram of interval variation series with equal intervals, the boundaries of the intervals are plotted on the abscissa axis, and the number of population units per given interval is plotted on the ordinate axis. Construct rectangles with equal bases. When constructing a histogram with unequal intervals, the boundaries of the intervals are also plotted on the abscissa axis, and the number of population units per unit width of the interval is plotted on the ordinate axis. Build rectangles

Example. Distribution of workers by length of service at the enterprise: 0-5 years - 210 people, 5-10 - 250 people, 10-15 - 300 people, 15-20 - 270 people, 20 - 25 years - 200 people.

As can be seen, the largest number of workers at the enterprise are with experience from 10 to 15 years, while the smallest number falls on people with experience of 20 to 25 years.

5.6. Graphs of interrelated indicators.

Graphs of interrelated indicators, one of which is equal to the product of the other two, can be built using the so-called "Varzar signs". The “Sign of Varzar” is built outside the system of rectangular coordinates in the form of a rectangle, the base of which is proportional to one factor-factor, and the height to another. The area of the rectangle is equal to the value of the third indicator, which is the product of the first two. By placing several rectangles related to different indicators side by side, it is possible to compare not only the size of the indicator - the product, but also the values of the indicators - factors.

Example. The following data are available for 2001 around the world: GNP - 46403 billion dollars, GNP per capita - 7570 dollars, average population - 6.1298 billion people. The relationship between these indicators can be represented as:

As can be seen from the graph, the total production of GNP in the world depends on the average population and on the production of GNP per capita.

6. Conclusion.

Having done this work, we really became convinced that graphs make statistical material more understandable and accessible even to non-specialists, simplify the perception of data. However, graphic images are not only illustrative, they are also analytical. With the help of a graphic image, it is possible to study the patterns of development of a phenomenon, to establish existing relationships.

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4.5. Structure Diagrams

The second large group of indicative graphs are structural diagrams. These are diagrams in which individual statistical populations are compared according to their structure, which is characterized by the ratio of different parameters of the population or its individual parts.

The simplest type of structural statistical diagrams are diagrams of specific weights, reflecting the structures of the compared populations according to the percentage of individual parts in them, distinguished by one or another quantitative or attributive characteristic (Fig. 13). These charts are obtained by converting a simple bar chart with subdivided bars. Bar charts of specific weights can reveal the economic essential features of many of the studied economic phenomena.

It is necessary to graphically depict the following data characterizing the structure of consumer spending in the Nth region for 2008-2009:

Table 6

Indicators
All consumer spending
Including:
Food
Non-grocery goods
Alcoholic drinks
Payment for services

Let us represent these data graphically in the form of a bar chart, the purpose of which is to show the change in the share of consumer spending of the population over two years.

Rice. 13. Dynamics of the share of consumer spending in the N-th region for 2008-2009

Significant advantages of strip structural diagrams in comparison with other types are their large capacity, the ability to reflect a large amount of useful information in a small space.

Another widely used method of graphical representation of the structure of statistical data is the compilation of structural pie or pie charts (Fig. 14). Pie charts are conveniently constructed as follows: the entire value of the phenomenon is taken as one hundred percent, and the percentages of individual parts are calculated. The circle is divided into sectors in proportion to the parts of the depicted whole. Thus, 1% accounts for 3.6 degrees. To obtain the central angles of the sectors depicting the proportions of parts of the whole, it is necessary to multiply their percentage by 3.6 degrees. Pie charts allow not only to divide the whole into parts, but also to group individual parts, giving, as it were, a combined grouping of shares according to two criteria (see Fig. 14).

Consider the construction of a pie chart according to the data presented in Table 7.

Table 7

The number of TV sets in the urban family of the N-th region in 2009

Number of TVs	no one			three or more
Share of the group to the total, (%)

The construction of a pie chart begins with determining the central angles of the sectors. To do this, we multiply the percentage expression of individual parts of the population by 3.6 degrees, i.e. 2 3.6 \u003d 7.2 o; 50 3.6 \u003d 180 o; 39 3.6 \u003d 140.4 o; 9 3.6 \u003d 32.4 o. According to the found values of the angles, the circle is divided into the corresponding sectors (Fig. 14a).

Rice. 14 a. The share of the number of TVs in the urban family of the N-th region in 2009 (a simple structural diagram)

Rice. 14 b. The share of the number of TV sets in the urban family of the N-th region in 2009 (structural diagram with grouping of shares)

On fig. 14 a, b shows two options for a structural pie chart: a) simple; b) with a grouping of shares.

Option b) in addition to the general division, shows two specific groups of families:

families with two or more TVs;

families with fewer than two television sets.

This type of chart is convenient for highlighting individual, most typical population groups. So, in this case, this is a group of families with less than two TVs.

Each share (sector, group of sectors) selected from the circle is built on the bisector of the common angle of the share, i.e. the center of the arc of this share belongs to the bisector and is located at a given distance from the common center of the diagram. With a large number of shares, the grouping gives good results, allowing you to better distinguish the necessary elements of the population by their weight.

Pie charts look convincing when there are significant differences in the compared structures, and when there are small differences, they may not be expressive enough.

4.6. Diagrams of dynamics

Dynamic diagrams are built to depict and make judgments about the development of a phenomenon in time. In the series of dynamics, many diagrams are used to visualize phenomena: bar, strip, square, circular, linear, radial, and others. The choice of the type of diagrams depends mainly on the characteristics of the source data, on the purpose of the study. For example, if there is a series of dynamics with several unequal levels in time (1913, 1940, 1950, 1980, 2008, 2010), then bar, square or pie charts are often used for clarity. They are visually impressive, well remembered, but not suitable for depicting a large number of levels, since they are cumbersome, and if the number of levels in a series of dynamics is large, then it is advisable to use line diagrams that reproduce the continuity of the development process in the form of a continuous broken line. In addition, line charts are convenient to use: when the purpose of the study is to depict the general trend and nature of the development of the phenomenon; when it is necessary to display several time series on one graph in order to compare them; when the most significant is the comparison of growth rates, not levels.

To build line charts, a system of rectangular coordinates is used. Usually, time is plotted along the abscissa axis (years, months, etc.), and scales are applied along the ordinate axis to display phenomena or processes. Particular attention should be paid to the scale of the coordinate axes, since the general view of the graph depends on this. Ensuring balance, proportionality between the coordinate axes is necessary in the diagram, since imbalance gives an incorrect image of the development of the phenomenon. If the scale for the scale on the abscissa axis is very stretched compared to the scale on the ordinate axis, then fluctuations in the dynamics of phenomena stand out little, and vice versa, an exaggeration of the scale along the ordinate axis compared to the scale on the abscissa axis gives sharp fluctuations. If there are no data for some years in the time series, this should be clarified when plotting. Equal time periods and level sizes should correspond to equal scale segments.

Consider building a line chart based on the data in Table 8

Table 8

Dynamics of the gross harvest of grain crops in the region for 2000-2009


Million tons

The image of the dynamics of the gross harvest of grain crops on a coordinate grid with an inextricable scale of values starting from zero is hardly advisable, since 2/3 of the diagram field remains unused and does not give anything for the expressiveness of the image. Therefore, under these conditions, it is recommended to build a scale without a vertical zero, that is, the scale of values breaks near the zero line and only a part of the possible graph field falls on the diagram. This does not lead to distortions in the image of the dynamics of the phenomenon, and the process of its change is drawn more clearly by the diagram (Fig. 15).

Rice. 15. Dynamics of the gross harvest of grain crops in the region for 2000-2009

Often, several curves are shown on one line chart, which give a comparative description of the dynamics of various indicators or the same indicator in different countries. An example of a graphical representation of several indicators at once can be fig. 16.

Rice. 16. Dynamics of production of nickel and zinc in the region for 2000-2009

Linear charts with a uniform scale have one drawback that reduces their cognitive value. This disadvantage lies in the fact that a uniform scale allows you to measure and compare only the absolute increases or decreases in indicators reflected in the diagram over the period under study. However, when studying the dynamics, it is important to know the relative changes in the studied indicators compared to the achieved level or the rate of their change. It is the relative changes in economic indicators in dynamics that are distorted when they are depicted on a coordinate diagram with a uniform vertical scale. In addition, in conventional coordinates, it loses all clarity and even becomes impossible to depict time series with sharply changing levels, which usually take place in time series over a long period of time.

In these cases, the uniform scale should be abandoned and the graph based on a semi-logarithmic system.

A semilogarithmic grid is a grid in which a linear scale is plotted on one axis and a logarithmic one on the other. In this case, the logarithmic scale is applied to the ordinate axis, and the abscissa axis has a uniform scale for counting time according to the accepted intervals (years, quarters, months, days, etc.). The technique for constructing a logarithmic scale is as follows: you need to find the logarithms of the original numbers; draw an ordinate and divide into several equal parts. Then put on the ordinate (or a parallel line equal to it) segments proportional to the absolute increments of these logarithms. Next, write down the corresponding logarithms of numbers and their antilogarithms, for example (0.000; 0.3010; 0.4771; 0.6021; ...; 1.000, which gives 1, 2, 3, 4 ..., 10). The resulting antilogarithms finally give the desired scale on the ordinate. The logarithmic scale is best understood with an example.

Let's say we need to show on a graph the dynamics of electricity production in the region for 1985 - 2009, over these years it has increased by 9.1 times. To this end, we find the logarithms for each level of the series (see Table 9).

Table 9

Dynamics of electricity production in the region for 1975 - 2004 (billion kWh)

Having found the minimum and maximum values of the logarithms of electricity production, we build a scale in such a way that all the data fit on the graph. In accordance with the scale, we find the corresponding points, which we will connect with straight lines. As a result, we get a graph (Fig. 17) using a logarithmic scale on the y-axis.

Rice. 17. Dynamics of electricity production in the region for 1980-2009

Dynamic diagrams also include radial diagrams built in polar coordinates and designed to reflect processes that are rhythmically repeated in time. Most often, these charts are used to illustrate seasonal fluctuations, and in this respect they have an advantage over statistical curves. Radial charts are divided into two types: closed and spiral. These two types of diagrams differ from each other in the construction technique, it all depends on what is taken as the reference base - the center of the circle or the circle.

Closed diagrams reflect the entire intra-annual cycle of the dynamics of one year. Their construction boils down to the following: a circle is drawn, the monthly average is equal to the radius of this circle, then the whole circle is divided into twelve equal sectors by drawing radii, which are depicted as thin lines. Each radius represents a month, with the arrangement of the months similar to a clock face. At each radius, a mark is made in a certain place, according to the scale, based on the data for the corresponding month. If the data exceeds the average annual level, then the mark is made outside the circle on the continuation of the radius. Then the marks of different months are connected by segments.

It is necessary to depict the volume of issued certificates of deposit by months of the year using a closed diagram (Fig. 18).

Table 10

Volume of certificates of deposit issued at the beginning
months for 2009

	Deposit certificates - total, million rubles

Continuation of the table. 10

Rice. 18. Volume of certificates of deposit issued in 2009

If a circle is taken as the base of reference, such diagrams are called spiral diagrams. Spiral charts differ from closed ones in that in them December of one year is connected not with January of the same year, but with January of the next year. This makes it possible to depict the entire time series for several years as a single curve. Such a diagram is especially illustrative when, along with the seasonal rhythm, the series exhibits a steady increase from year to year.

To display the dependence of one indicator on another, a relationship diagram is built. One indicator is taken as X and the other as Y (i.e. a function of X). A rectangular coordinate system with scales for indicators is built, in which a graph is drawn. Figure 19 shows the relationship between the cost of fixed assets and the level of costs for the sale of products.

Rice. 19. Dependence of the level of costs for the sale of products on the cost of fixed production assets

The graph constructed above shows that with an increase in the cost of fixed production assets, there is an increase in the cost of selling products and this dependence of the two indicators will be determined by a linear relationship.

4.7. Statistical maps

Statistical maps are a type of graphical representation of statistical data on a schematic geographical map, characterizing the level or extent of distribution of a particular phenomenon in a certain territory.

The means of depicting territorial distribution are hatching, background coloring or geometric shapes. There are cartograms and cartograms.

A cartogram is a schematic geographical map on which shading of varying density, dots or coloring of varying degrees of saturation shows the relative intensity of an indicator within each unit of the territorial division plotted on the map (for example, population density by region or republic, distribution of regions by grain yield crops, etc.). Cartograms are divided into background and point.

Background cartogram - a type of cartogram, on which shading of various density or coloring of various degrees of saturation shows the intensity of any indicator within a territorial unit. Dot cartogram - a kind of cartogram, where the level of a phenomenon is depicted using dots. A point depicts one unit of the population or a certain number of them to show the density or frequency of occurrence of a particular feature on a geographical map.

The second large group of statistical maps are chart diagrams, which are a combination of diagrams with a geographical map. Chart figures (bars, squares, circles, figures, stripes) are used as figurative signs in cartograms, which are placed on the contour of a geographical map. Cartograms make it possible to reflect geographically more complex statistical and geographical constructions than cartograms.

The development of computer technology and applied software has made it possible to create geographic information systems (GIS), which represent a qualitatively new stage in the graphical presentation of information. A geographic information system is a system that provides the collection, storage, processing, access, display and distribution of spatially coordinated data. GIS includes a large number of graphical and thematic databases in combination with model and calculation functions that allow you to present information in a spatial (cartographic) form, to obtain multi-layered electronic maps of the region at various scales. According to the territorial coverage, the following types of GIS are distinguished: global, subcontinental, state, regional and local. The subject orientation of a GIS is determined by the tasks it solves, which may include resource inventory, analysis, evaluation, monitoring, management, and planning.

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Bar charts– are a set of columns in a coordinate system designed to display discrete data. Bar charts are used to display the results of comparing the same indicator under different conditions (for example, the results of sociological surveys). Bar charts should be represented as individual bars of equal width because they represent discrete data and should never be linked by a line.

Particular attention must be paid to the scale bar: it must exactly correspond to the countdown from zero. Otherwise, the graphic image will distort the data. If initially it is necessary to introduce a break in the scale bar (starting not from zero, but from a certain value), it is necessary to designate a "zigzag" on this axis.

Rice. Bar Chart Example

If charts are used to represent discrete data, then histograms are used to represent continuous (frequency distribution). Histograms should be formatted as bars touching each other.

4. Building and formatting charts.

Collect tabular data.

2. Select the data area along with one header line as shown in the figure:

3. Tue but vka ® Dia G Plot ® Select chart type: schedule

In the input field " X-axis labels » enter the range where the labels for the X-axis values are located. To do this, you must:

Press the button with the red arrow, which is located on the right side of the input line;

Select a range (values of the column " Volume of production»);

Click Enter.

In the window that appears, enter: the name of the chart, labels under the axes X And Y , as shown in the figure:

® Press " Ready ". We get:

The resulting graph image is not an acceptable result. The graph practically does not reflect the information presented in the table, for which it was intended to visually display.

The chart needs to be enlarged. To do this, it is necessary to select the diagram by clicking on it with the mouse, and the mouse click must be made on the area of the diagram free from graphic elements. In this case, black square dots appear around the chart (see the figure above), with the help of which you can resize the chart. If you now drag the upper left corner point, it will be possible to increase or decrease the size of the diagram.

After increasing the size of the diagram, it is necessary to change the sizes of individual diagram blocks in such a way as to highlight the information presented in the diagram and give it a semantic load.

To do this, you need to reduce the font size (size) of the text in the text blocks:

Select a test block;

Set the font size as shown in the picture:

After changing the font of the text blocks, we get the following image.

Now it is necessary to resize the graphic blocks in such a way as to present the graphic information in the best possible way. You need to resize the plotting area (chart area) and the data series label area (legend). Necessary:

1. Select the legend area, as shown in the figure below:

2. Resize the label area (see the figure below) by dragging the corresponding black dot to resize (zoom).

3. Select the area for plotting the diagram.

4. Change the dimensions of the chart construction area (see below):

From the figure above, you can see that the background of the plotting area (gray) does not contribute to a better perception of graphic information. It must be changed to white or abandoned altogether.
from background:

1. Select the area for plotting the diagram.

2. Call the properties of the plotting area (double-click on the chart area or call the context menu by right-clicking ® Construction area format )

3. In the settings dialog that opens, in the section " fill " install " transparent » and press OK. The result is shown in the figure below:

From the resulting image of the diagram (see above), it can be seen that it is necessary to change the color of the graphs to black, as well as the thickness of the lines. It is recommended to use the black color of the graphs if this graph or diagram is planned to be printed on a black-and-white printer.

Sequencing:

1. Select the graph as shown in the figure (Move the mouse pointer to one of the graphs (the pointer must be located directly on the line) ® Click once.

If not the entire graph is selected, but only a part of it, then you need to adjust the appearance of the diagram in accordance with the sample, as shown in the figure:

Working with Pie and Column Charts is done in the same way as with charts. The only exception is the way the pie chart area is selected. The plotting area is rectangular, while on the screen it looks round. This is the source of the difficulty. In order to select the area for constructing a pie chart, imagine that the pie chart is inscribed in a square or rectangle and click on one of the corners of this triangle.

One of the most common and fairly universal methods for displaying the results of analyzes is the construction of histograms, or bar charts. In granulometric analysis, diagrams are often used, since they are the first stage in processing the results obtained. The diagram characterizes the distribution of fractions in the sample in the form of columns. The abscissa axis shows the size of the fractions (mm), the ordinate axis shows the percentage of grains in this fraction (%).

The constructed diagram is shown in Figure 1. After granulometric analysis and subsequent calculation, the following data were obtained:

- 0,13-0,16-1,2 %
- 0,16-0,2-10,8 %
- 0,2-0,25-9,3 %
- 0,25-0,32-18,8 %
- 0,32-0,4-14,0 %
- 0,4-0,5-22,7 %
- 0,5-0,6-13,7 %
- 0,6-0,8-8,8 %
- 0,6-0,8-0,8 %.

From the diagram, we can judge which fractions predominate in the sample. In our case, in the amount of 22.7% and 18.8%, dimensions from 0.4-0.5 mm prevail. and 0.25-0.32 mm. respectively. Based on these data, it can be concluded that one fraction predominates in the rock and its dimensions correspond to medium-grained sand.

The histogram allows you to clearly identify the predominant fraction, qualitatively assess the degree of sorting of the rock, determine the modal, i.e. the most common grain size.

Construction of a cumulative curve

One of the important methods of graphical processing of granulometric analyzes is the construction of a cumulative (total) curve. In order to build it, we need to fill in the last column of table 7. It is calculated as follows: the smallest fraction is taken as the initial fraction - clay (0.01-0.05 mm.). Then the percentage of the next largest fraction (0.05-0.1 mm) is added to this fraction. Thus, from fraction to fraction, the values increase, and by the last available fraction, the value will approach 100%.

The constructed diagram is shown in Figure 2. On the abscissa, we plot the sizes of the fractions on a logarithmic scale (mm), on the ordinate - the cumulative percentage (%). And then you need to build a curve from the points. In our case, the first three points, which correspond to fractions of sizes 0.01-0.05 mm., 0.05-0.1 mm. and 0.1-0.13 mm. have 0 cumulative percentage. The fourth point, which corresponds to a fraction of 0.13-0.16 mm. has 1.2 total percentage. We need to mark this point. The fifth point corresponds to a fraction of 0.16-0.2 mm. we plot this value on the abscissa, on the ordinate we plot 12%. The next point corresponds to a fraction of 0.2-0.25 mm. We plot this value along the abscissa in a logarithmic scale, the total percentage is 21.3%. The next point corresponds to a fraction of 0.25-0.32 mm. this value is denoted on the x-axis, the total percentage is 40.1%. Further, the point corresponds to a fraction of 0.32-0.4 mm. this value must be plotted on a logarithmic scale along the x-axis, the total percentage is 54.1%. Then the point corresponds to a fraction of 0.4-0.5 mm., This value is plotted along the abscissa, the cumulative percentage is 76.8%. The next point corresponds to a fraction of 0.5-0.6 mm., Its cumulative percentage is 90.5%, we plot these values along the corresponding axes. The next fraction corresponds to the size of 0.6-0.8 mm, its total percentage is 99.3%. And, finally, the last point corresponds to a fraction of 0.8-1 mm in size, its cumulative percentage is 100.1%. The resulting points must be connected with a smooth line.

According to the shape of the straight line, one can judge the degree of sorting of the rock, some scientists argue that the appearance can also be said about the dynamics of the transfer medium. The cumulative curve is important not only as a form of graphic representation of analytical data; the main thing is that it is used to determine a number of parameters that characterize the structure of the rock and, above all, the average grain size and sorting coefficient.

General theory of statistics Shcherbina Lidiya Vladimirovna

17. Bar charts.

The most common comparison charts are bar charts. Each bar depicts the value of a separate level of the studied statistical series. When constructing bar charts, it is necessary to draw a system of rectangular coordinates in which the bars are located. The bases of the columns are located on the horizontal axis, the size of the base is determined arbitrarily, but is set the same for everyone. The scale that determines the scale of the columns in height is located along the vertical axis. The value of each vertical column corresponds to the size of the statistical indicator displayed on the graph. All columns have only one dimension as a variable. Placement of columns in the graph field can be different:

1) at the same distance from each other;

2) close to each other;

3) in private imposition on each other.

Varieties of bar charts are the so-called strip (or strip) charts. The scale scale is located horizontally at the top and determines the size of the strips along the length. Bar and bar charts are essentially interchangeable as a way of representing statistical data graphically.

A variety of bar (ribbon) charts are directional charts. They differ from the usual two-sided arrangement of columns or stripes and have a scale origin in the middle. Analysis of directional diagrams allows us to draw meaningful conclusions. The group of bilateral includes charts of pure deviations. In them, the stripes are directed in both directions from the vertical zero line: to the right - for growth, to the left - for decrease.

The most expressive and easily perceptible is the method of constructing comparison diagrams in the form of figure-signs. In this case, statistical aggregates are represented not by geometric figures, but by symbols or signs.

The most important feature of any chart is the scale. Therefore, in order to correctly construct a figure chart, it is necessary to determine the unit of account. As the latter, a separate figure (symbol) is taken, which is conditionally assigned a specific numerical value. And the statistical value under study is represented by a separate number of figures of the same size.

The main structure of structural diagrams is a graphical representation of the composition of statistical populations, characterized as the ratio of different parts of each of the populations. The composition of the statistical population graphically can be represented using both absolute and relative indicators.

The graphic representation of the composition of the population in terms of absolute and relative indicators contributes to a deeper analysis and allows for international comparisons and comparisons of socio-economic phenomena.

From the book General Theory of Statistics author Shcherbina Lidia Vladimirovna

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