# GRAPHICAL REPRESENTATION OF STATISTICAL DATA

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Statistics should be presented so that they can be used. There are 3 main forms of reporting statistics:

text - inclusion of data in the text,

tabular - presentation of data in tables,

graphic - expression of data in the form of graphs.

The text form is used with a small amount of digital data.

The tabular form is used most often, as it is a more effective form of presentation of statistical data. Unlike mathematical tables, which, according to the initial conditions, allow one or another result to be obtained, statistical tables tell in the language of numbers about the objects being studied.

Statistical Table- a system of rows and columns in which statistical information on socio-economic phenomena is presented in a certain sequence and connection.

Table 2. Foreign trade of the Russian Federation for 2000 - 2006, billion dollars

with foreign countries

For example, in table. 2 provides information on Russia's foreign trade, expressing which in text form would be ineffective.

Distinguish subjectandpredicatestatistical table. The subject shall indicate the characterized object - either units of the population, or a group of units, or the population as a whole. The predicate describes the subject, usually in numerical form. Requiredheadinga table in which it is indicated to which category and to what time the data in the table belongs.

According to the nature of the subject, statistical tables are divided into simple,groupandcombinational. In the subject of a simple table, the object of study is not divided into groups, but either a list of all units of the population is given, or the population as a whole is indicated (for example, Table 11). In the subject of the group table, the object of study is divided into groups according to one attribute, and in the predicate, the number of units in the groups (absolute or percentage) and summary indicators for the groups (for example, Table 4) are indicated. In the underlying combination table, the population is divided into groups not by one, but by several criteria (for example, Table 2).

When building tables, you must be guided by the following general rules.

The subject of the table is located in the left (less often - upper) part, and the predicate - in the right (less often - lower).

The column headings contain the names of the indicators and their units.

The final line completes the table and is located at its end, but sometimes it happens first: in this case, the record “including” is made in the second line, and the subsequent lines contain the components of the final line.

Digital data is recorded with the same degree of accuracy within each column, while the bits of numbers are located under the bits, and the integer part is separated from the fractional comma.

The table should not contain empty cells: if the data is equal to zero, then the “-” sign (dash) is put, if the data is not known, then the record “no information” is made or the “...” sign (ellipsis) is put. If the value of the indicator is not equal to zero, but the first significant digit appears after the accepted degree of accuracy, then a record of 0.0 is made (if, say, an accuracy level of 0.1 was adopted).

Sometimes statistical tables are supplemented by graphs, when the goal is to emphasize some feature of the data, to compare them. The graphical form is the most effective form of data presentation in terms of their perception. With the help of graphs, the visibility of the characteristics of the structure, dynamics, the relationship of phenomena, their comparison is achieved.

Statistical graphs- these are conditional images of numerical quantities and their relationships through lines, geometric shapes, patterns or geographical map diagrams. The graphical form facilitates the consideration of statistical data, makes them visual, expressive, visible. However, the graphs have certain limitations: first of all, the graph cannot include as much data as can be included in the table, in addition, the graph always shows rounded data - not accurate, but approximate. Thus, the graph is used only to depict the general situation, and not the details. The last drawback is the complexity of graphing. It can be overcome using a personal computer (for example, “Chart Wizard” from the packageMicrosoftOfficeExcel).

By the method of constructing graphics are divided into charts,cartogramsandchart diagrams.

The most common way to graphically display data is diagrams that are of the following types: linear, radial, point, planar, volumetric, curly. The type of diagrams depends on the type of data presented and the task of construction. In any case, the chart must be accompanied by a heading - above or below the chart field. The heading indicates which indicator is depicted, in which territory and for how long.

Line graphs are used to represent quantitative variables: characteristics of the variation of their values, dynamics, relationships between variables. Data variation is analyzed using polygon distribution,cumulative(less than than curve) andogive(curve "more than"). The distribution polygon is discussed in topic 4 (e.g., Fig. 5.). To build cumulative values, the values ​​of the varying attribute are plotted along the abscissa, and the accumulated totals of frequencies or frequencies (fromf1to ∑f) To build ogives, the accumulated frequency totals in the reverse order (from ∑fbeforef1) Cumulate and ogive according to the table. 4. depict in fig. one. Fig. 1. Cumulate and ogiva distribution of goods by value of customs value

The use of line graphs in dynamics analysis is discussed in topic 5 (e.g., Fig. 13), and their use for link analysis is discussed in topic 6 (e.g., Fig. 21). Topic 6 also discusses the use of scatter plots (e.g., Figure 20).

Line charts are divided into one-dimensionalused to represent data on a single variable, andtwo-dimensional- in two variables. An example of a one-dimensional linear graph is a distribution polygon, and a two-dimensional one is a regression line (e.g., Fig. 21).

Sometimes, with large changes in the indicator, they resort to a logarithmic scale. For example, if the indicator values ​​vary from 1 to 1000, then this can cause difficulties in plotting. In such cases, they pass to the logarithms of the indicator values, which will not vary so much: lg 1 = 0,lg 1000 = 3.

Among planarCharts by frequency of use are highlighted by bar charts (histograms), on which the indicator is presented in the form of a column whose height corresponds to the value of the indicator (eg, Fig. 4).

The proportionality of the area of ​​a particular geometric figure to the value of the indicator underlies other types of planar diagrams: triangular,square,rectangular. You can also use the comparison of the area of ​​the circle - in this case, the radius of the circle is set.

Ribbon chartrepresents indicators in the form of horizontally elongated rectangles, but otherwise does not differ from the bar chart.

Of planar charts often used pie chart, which is used to illustrate the structure of the studied population. The entire population is taken as 100%, it corresponds to the total area of ​​the circle, the area of ​​the sectors correspond to parts of the population. We construct a sector diagram of the structure of foreign trade of the Russian Federation in 2006 according to the table. 2 (see Fig. 2). When using computer programs, sector diagrams are built in three-dimensional form, that is, not in two, but in three planes (see Fig. 3).  Fig. 2. A simple pie chart Fig. 3. Volume pie chart

Curly (picture) diagrams enhance the visibility of the image, since they include a picture of the depicted indicator, the size of which corresponds to the size of the indicator.

When plotting a graph, everything is equally important - the correct choice of a graphic image, proportions, compliance with the rules for designing graphs. These issues are covered in more detail in and.

Cartograms and cartographic diagrams are used to depict the geographical characteristics of the phenomena studied. They show the location of the phenomenon under study, its intensity in a certain territory - in the republic, region, economic or administrative district, etc.. The construction of cartograms and cartographic diagrams is considered in specialized literature, for example.

# How to present statistics in graphical form

Using lines, bars, and symbols in a chart, you can represent a lot of different data. A graphical representation of the data allows you to structure it and facilitates understanding and analysis. For different types of data, different types of graphical representations are suitable, therefore, for the effective presentation of data and the creation of interesting and memorable presentations, it is necessary to know what tools are best used for certain data.

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