GRAPHIC REPRESENTATIONS IN STATISTICS.

 

Diagrammatic and graphic representation of data

The data in statistics are generally based on individual observations. Some basic terms that are necessary for an understanding of biological and agricultural data are:

Sample and population

The selection of a part of a population to represent the whole population is known as sampling and the part selected is known as sample. The object of sampling is to get information regarding the population from which the sample is obtained. Suppose, there are 500 girls in a college, if we want to know the average weight of those girls, we will weigh each girl and will get information about all the 500 girls. The average will be obtained by dividing the total weight of the girls by the number of girls. The population is the weight of the entire group of 500 girls. However, we can save the time and labour by taking only 50 girls out of 500 girls and obtain the average of this part of the total population. The average of 50 girls reasonably is representative of average weight of 500 girls. In this case weight of 50 girls is the sample. Examples: We look at a handful of grain from a bag to evaluate the quality of rice, A drop of blood is tested for diseases like malaria, typhoid etc.

In statistics, population always means the total number of individual observations from which inferences are to be made at a particular time. A sample represents the small collection of the population which has actually been observed. For example, all plants in a wheat field represent a population. Whereas individual observations on ten high yielding plants from this population refer to a sample. Populations may be finite or infinite. If a population of values consists of a fixed number of these values, the population is said to be finite. For example, the number of plants in a quadrat, the number of wheat plants in a plot and the number of patients in a hospital etc. On the other hand, population in which it is theoretically impossible to observe all the values, is an infinite one. An infinite population is unlimited in size. For example, the number of phytoplanktons in a pond, the number of RBCs in the human body and so on.

If we have collected data on only one variable we have a “univariate” population.

However, if two variables are measured (say the price of a certain commodity and the quantity demanded) we have a “bivariate” population. When more than two variables are measured on every individual, it is “multivariate” population.

Variable

The data collected for statistical analysis do not consist of observations that are identical, since there would be little reason to study such a variation. The data counted or measured for analysis purposes will represent the varying values of variable, i.e. a characteristic that shows variation. Any quantity or quality liable to show variation from one individual to the next in the same population is known as variable. An individual observation of any variable is known as variate. Examples: the plant height, heights of adult males, the weights of preschool children and the ages of patients seen in a dental clinic.

Parameters

Measures describing the characteristic of a population are called parameters. For example: the mean pod length of all mungbean varieties growing in a field is 60mm. In this case, 60mm is the characteristic of the population of all mungbean varieties and can be called as population parameter. Greek letters are usually used to denote parameters. The population mean is represented by µ.

Types of data

Primary data is original and first-hand information. It can be collected through direct personal interview, mailed questionnaires or information from correspondents.

Secondary data is those data collected from second person. It can be collected from Government publications, report of Committees and Commissions, newspapers, journals, magazines, annual reports, etc.

Summarization of data through frequency distribution

One of the most important aspects to any data presentation or data analysis is summarizing the available data in a condensed and meaningful form. This can be done with the help of frequency distribution tables and graphical representation. Let’s look at summarizing the data with the help of frequency distribution tables.

Summarizing of data: Typically in any given problems or in a sample data we have sets of numbers thrown together which do not give out any specific output unless segregated. The method of classifying the available data so as to give out a desired output or a meaningful result is called “Summarizing”. This forms a part of the study called Descriptive Statistics. Descriptive Statistics talks about arranging and displaying numerical information from which conclusion can be drawn.

Frequency Distribution: The technique used in arranging, sorting and depicting relevant data through grouping of data into categories, showing the number of observation in each of the non-overlapping classes is called as frequency distribution. For example let us look at the recently published report by the WHO on the number of AIDS related death in our country. The table put forth data on the age group of people and the number in each of these age groups.

Graphic representation and the graphic analysis

The graphic representations are used for evident imagination of statistical quantities they allow to analyze them deeper.

The graphic representation can be built both after absolute and after relative quantities.

Using the graphic method, it is important to know that the type of graphic representation must strictly answer the maintenance of every index.

For construction of graphic representations the following quantities are used:

Relative quantities are:

     – intensive indices

– extensive indices

– index of correlation

– index of evidence

Absolute quantities

Intensive quantities – 4 types of diagrams:

·        column

·        linear

·        mapgram  

·        mapdiagram

Extensive quantities: (they characterize the structure) sector or inwardly-column diagram.

Indices of correlation: the same diagrams, that for intensive quantities (column and linear diagrams, mapgram, mapdiagram).

Indices of evident:  the principles of graphic representation are the same, that for intensive quantities.

Column diagrams – for illustration of homogeneous, but not interconnected indices. They represent the static’s of the phenomena.

Linear diagrams – for the representations of dynamics of that or other phenomenon (a typical example is a temperature curve, change of birth-rate, death rate level).

Radial diagram – is built on the system of polar co-ordinates of the phenomenon representations during the close cycle of time (days, week, year). For example: structure of morbidity or cause of mortality, where in a circle every cause of mortality, depending on its percent occupies a certain sector.

Mapgram is the representations of statistical quantities on a geographical map (or scheme of card).

Absolute and other indices can be marked.

Mapdiagram is the representations of different types of diagrams on the geographical map.

Common rules of construction of graphic representations:

·        every graphic representation must have the name, where its contest, time and place is mentioned;

·        it must be built in a certain scale;

·        for every graphic representation explanation of colored application must be given (as conditional denotations or shading).

During the choosing of graphic representations type, it’s necessary to know that it must strictly answer to the essence of the represented index.

Principles of construction and application of square diagrams (linear, column, rectangular, sector, radial).

Linear diagram is used for illustration of the frequency phenomena which changes with time, that for the representations of the phenomena dynamics.

The base of this diagram is the rectangular system of co-ordinates. For example: on abscising axis – Х – segments are put aside on a scale, on a y-axis –  indices of morbidity (х : y = 4: 3).

Column diagram (rectangular) is used for illustration of homogeneous, but not connected between themselves intensive indices. It represents dynamics or static of the phenomena.

At construction of this kind of diagram columns are drawn, the height of which must suit the quantities of the represented indices taking the scale into account. It is necessary to take into account that the wideness of all the columns and also the distance between them must be identical and arbitrary. Columns on a diagram can be vertical or horizontal. For example: growth of number of beds in permanent establishment from 1990 to 2003 year.

Sector diagram is used for illustration of extensive indices, which characterize the structure of the phenomenon, thus they give imagination about specific gravity of the phenomena in common.

The circle is taken as 100 % (if indices are shown in %) thus 1 % equal to 3,6⁰ circumferences. With the help of protractor the segments, which suit the size of an index are put aside on a circle.

For example: among all infectious diseases a measles had 28,6 % (28,6×3,60= 1030), and other infections  – 71,4 % (71,4×3,60=2570).

With the help of protractor the segments, which suit the size of every index are put aside on a circle. The found points of circumference are connected with the center of circle. Separate sectors in the circle are the parts of the phenomenon, which we determine.

In place of sector it is possible to use an inwardly-column diagram. Then for 100 % the whole height of column is taken and the extensive indices are put in the proper scale units, which give, in essence, the whole one.

Radial diagram is the type of the linear diagram built on polar co-ordinates.

At the construction of radial diagram in the role of abscising axis – Х is the circle divided on the identical number of parts, according to the spans of time of that or another cycle.

A y-axis is the У- radius of circle or its continuation.

So, for the radius of circumference the medial quantity of time cycle is phenomenon, which we analyze is taken. The amount of radiuses is equal to the time domains of cycle, which we study:

·        12 radiuses – at the study of the phenomena during a year

·        7 radiuses – at the study of the phenomena during a week.

The beginning of radiuses marking is accepted to begin from radius, which answers to 12 hours and to continue on a hour – hand.

 

Results of examinations after their statistical processing can given as graphic representations, on which numerical numbers are presented as drawing. Schedules give a general characteristic of the phenomenon and define its general laws, enable to analyze the given researches more deeply.

 

They facilitate comparison of parameters, give imagination about structure and character of connection between the phenomena, specify their tendencies.

Therefore ,  graphic demonstration we often  connect  with  the graphic analysis for which the graphic representation serves not only means of demonstration of results and conclusions research, but also means of the analysis of the received materials, revealing of internal connections and laws.

 

At construction of schedules character of the data which are subject to a graphic representation, purpose of schedules (demonstration at conference, lectures, a reproduction in scientific work, etc.), the purpose of the schedule (evidently to show the received results or only to emphasize, allocate any law or the fact), a level of an audience before which the schedule is shown are taken into account.

The choice will depend on all it is the following as a graphic representation, color, the number, a proportion of a print, etc. In all cases schedules should be clear, convenient and easy for reading.

 

In medical statistical researches linear diagrams, plane diagrams, cartograms and linear or coordinate are used.

 

LINEAR DIAGRAMS are schedules on which numerical values are displayed by curves which allow to trace dynamics of the phenomenon in time or to find out dependence of one attribute on another (Fig. 2.1).

 

Fig.2.1 Age mortality rate of the population in Ukraine(Ukrainian  Center of  medical statistics, Kyiv,1999)

 

Whether on linear diagrams with two and a plenty of curves probably also comparison of numbers in two the greater number of dynamic lines, and also an establishment of dependence of changes of fluctuations which occurs in the other number line.

 

Linear diagrams are  made  according to system of rectangular coordinates where the horizontal scale is postponed at the left – to the right on a line of abscissas (X), and vertical – from below – upwards on a line which is called as ordinate (Y). The obligatory requirement of construction of any schedule is scale, that is the image on drawing should be reduced, compared with corresponding figures.

Contrast to linear diagrams which describe dynamics of any process, plane diagrams are used in the case when it is necessary to represent the statistical phenomena or the facts, independent one from another.

The most simple example of plane diagrams is the diagram as rectangular or figures. Digital numbers on plane diagrams average represented by geometrical figures – rectangular, squares. These diagrams are used for demonstration and popularization of the resulted data, and also in cases if it is necessary to represent structure of the phenomenon on one of the moments of supervision.

For example, age type fallen ill or structure of disease in any settlement.

Fig. 2.2 Age structure of the population in Ukraine, 1990, % (the part of each age layer was determined to all population).

 

In long-pillar diagrams digital numbers are represented by rectangular columns with an identical basis and different height.

The height of a rectangular corresponds to the relative value of the phenomenon which is studied. For construction a long-pillar diagram we use a scale according to which it is possible to determine the height of each column.

Long-pillar diagrams serve for comparison of several sizes.  It is possible to rectangular which represent sizes, it is possible to place also on the plane diagram not on a vertical, and across and then there will be a tape diagram (Fig.4). In some cases the image of sizes as tapes (stirs) is more convenient, than as columns because it is easier to sign with each tape by a horizontal inscription.

With the aid of column and tape diagrams it is possible not only to compare different sizes, but also simultaneously to display structure of these numbers and to compare their parts. For example, long-pillar or tape diagrams which show distribution of diseases on the basic nosological forms, it is possible to show also percent of diseases among men and women.

For this purpose it is necessary (a figure or a tape) to divide each rectangular for two parts, any of which will correspond to digital number of disease among men and women.

In circular diagrams they use to display ratio of homogeneous absolute sizes.

They don’t use the area of a rectangular, but the area of a circle.

 

But  it is necessary to remember, that the areas of circles match up one another as squares of their radiuses, therefore at construction of circular diagrams we must  extract off the diagram sizes and on this basis to construct radius, and having radius, it is easy to describe a circle.

In a case if the circular diagram displays parts of the whole, it is necessary to display circles not separately one from another, and to impose against each other. The whole is possible also and its parts to submit as the circle divided on sectors – the sector diagram. At construction of the sector diagram all area of a circle is accepted for 100 %, and each sector occupies is the following part of the area which correspond to the necessary percent.

In practice for construction of sector diagrams it is possible to use not only the area of a circle, but also the area of a square and a rectangular.

 

Nevertheless, often it happens to divide is the following figures are harder than a circle and consequently they are rather seldom used as a basis of sector diagrams.

Radial or linear – circular diagram (Fig.2.3) are constructed on the basis of number coordinates in which the radius replaces vertical scale of diagrams which are based on system of rectangular coordinates.

The example of the radial diagram is a wind rose with the aid of which we represent on maps the change of a direction of a wind during any calendar period of time (month, year).

Radial diagrams are used for an illustration of seasonal fluctuations of any numbers, for example diseases or mortality rates.

These diagrams are constructed on a circle which center has12 radiuses. Each radius saws from a circle an arch in 30 (360/12=30) also represents ordinate of one of calendar months: January, March, etc.

As an initial zero point they take the center of a circle, and then on radiuses according to the scale chosen before render numbers which display intensity of seasonal fluctuations of the phenomenon in any of calendar months.

Having connected the marked points, we receive the closed line which enables to imagine seasonal fluctuations.

When building radial diagrams, it is necessary to remember a rule of calculation of radiuses from the top part of the diagram and in other words.

Fig. 2.3 The radial diagram.

Seasonal prevalence of mortality rate of the population of Kalinovsky district by Vinnitsya region (1984-1998 ,Ukraine).

 

Comparisons of the different phenomena according to the territorial attribute cartograms are built, if necessary. They represent geographical maps, on which with the aid of graphic symbols, where the intensity of distribution and grouping of the phenomenon (morbidity, mortality, etc.) for any period of time (Fig. 2.4) is shown.

 

Therefore they are better for building on simplified maps on which only administrative frontiers and some big settlements are shown. At construction of a cartogram the great value has grouping the phenomena which are displayed.

The most simple grouping is division of some parameters on group with parameters below average and group with parameters is higher than average. According to this division regions districts with parameters than will be shaded on a cartogram and below average – not shaded.

Fig. 2.4 Regional features of mortality from cancer in Ukraine.

 

Displays and Appraisals of Patterns

The stem-leaf plots discussed earlier in Section 3.3.1.2. have been replacing the histograms that were used for many years to display the shape and contents of dimensional data. Histograms are gradually becoming obsolete because they show results for arbitrary intervals of data rather than the actual values, and because the construction requires an artistry beyond the simple digits that can easily be shown with a typewriter or computer for a stem-leaf plot.

1. One-Way Graph

Data can always be displayed, particularly if the stem-leaf plot is too large, with a “one-way graph.” The vertical array of points on the left of Figure 5.2 is a one-way graph for the data of Table 3.1. In this type of graph, multiple points at the same vertical level of location are spread horizontally close to one another around the central axis. A horizontal line is often drawn through the vertical array to indicate the location of the mean. The horizontal line is sometimes adorned with vertical flanges so that it appears as  rather than  .The adornment is merely an artist’s aesthetic caprice and should be omitted because it can be confusing. The apparently demarcated length of the flange may suggest that something possibly useful is being displayed, such as a standard deviation or standard error.

2. Box Plot

If you want to see the pattern of dimensional data, the best thing to examine is a stem-leaf plot. To summarize the data, however, the best display is another mechanism: the box plot, which Tukey called a “box-and-whiskers plot.” Based on quantiles rather than “parametric” indexes, the box plot is an excellent way to show the central index, interquartile (50%) zone, symmetry, spread, and outliers of a distribution. The “invention” of the box plot is regularly attributed to John Tukey, who proposed1 it in

1977, but a similar device, called a range bar, was described in 1952 in a text by Mary Spear. 8 Spear’s horizontal “range bar,” reproduced here as Figure 5.3, shows the full range of the data, the upper and lower quartiles that demarcate the interquartile range, and the median.

Construction of Box — In the customary box plots today, data are displayed vertically with horizontal lines drawn at the level of the median, and at the upper and lower quartiles (which Tukey calls “hinges”). The three horizontal lines are then connected with vertical lines to form the box. The interquartile spread of the box shows the segment containing 50% of the data, or the “H-spread.” The box plot for the data of Table 3.1 is shown on the right side of Figure 5.2, using the same vertical units as the corresponding one-way graph on the left. For the boundaries of the box, the lower quartile is at 17 between the 14th and 15th rank, and the upper quartile is at 28 between the 41st and 42nd rank. The box thus has 28 as its top value, 21 as the median, and 17 at the bottom. The mean of 22.7 is shown with a + sign above the median bar.

The width of the horizontal lines in a box plot is an aesthetic choice. They should be wide enough to show things clearly but the basic shape should be a vertical rectangle, rather than a square box. When box plots are compared for two or more groups, the horizontal widths are usually similar, but McGill et al.9 have proposed that the widths vary according to the square root of each group’s size.

Construction of “Whiskers” — Two single lines are drawn above and below the box

to form the “whiskers” that summarize the rest of the distribution beyond the quartiles. The length of the whiskers will vary according to the goal at which they are aimed.

If intended to show the ipr95, the whiskers will extend up and down to the values at the 97.5 and 2.5 percentiles. For the 2.5 and 97.5 percentiles, calculated with the proportional method, the data of Table 3.1 have the respective values of 12 and 41. Because the upper and lower quadragintile boundaries may not be located symmetrically around either the median or the corresponding quartiles, the whiskers may have unequal lengths. In another approach, the whiskers extend to the smallest and largest observations that are within an H-spread (i.e., interquartile distance) below and above the box.

For many analysts, however, the main goal is to let the whiskers include everything but the outliers.

The egregious outliers can often be noted by eye, during examination of either the raw data or the stem-leaf plot. The box-plot summary, however, relies on a demarcating boundary that varies with different statisticians and computer programs. Tukey originally proposed that outliers be demarcated with an inner and outer set of boundaries that he called fences. For the inner fences, the ends of the whiskers are placed at 1.5 H-spreads (i.e., one and a half interquartile distances) above the upper hinge (i.e., upper quartile) and below the lower hinge (i.e., lower quartile). The outer fences are placed correspondingly at 3.0 H-spreads above and below the hinges. With this convention, the “mild” or “inner” outliers are between the inner and outer fences; the “extreme” or “outer” outliers are beyond the outer fence.

Tukey’s boundaries are used for box-plot displays in the SAS data management system,10 where the inner outliers, marked 0, are located between 1.5 and 3 H-spreads; the more extreme outliers, marked *, occur beyond 3 H-spreads. In the SPSS system,11 however, an “inner outlier” is in the zone between 1.0 and 1.5 H-spreads and is marked with an X; the “outer” (or extreme) outliers are beyond 1.5 H-spreads and are marked E.

In the data of Table 3.1 and Figure 5.2, the spread between the hinges at the upper and lower quartiles is 28 − 17 = 11. Using the 1.5 H-spread rule, the whiskers would each have a length of 1.5 Ч 11 = 16.5 units, extending from 0.5 (=17 16.5) to 43.5 (=28 + 16.5). Because the data in Table 3.1 have no major outliers, the whiskers can be shortened to show the entire range of data from 11 to 43. This shortening gives unequal lengths to the whiskers in Figure 5.2.

On the other hand, if boundaries are determined with the 1 H-spread rule, each whisker would be 11 units long, extending from a low of 6 (= 17 11) to a high of 39 (= 28 + 11). The lower value could be reduced, because the whisker need only reach the smallest value of data (11), but the upper whisker would not encompass the data values of 41 and 42, which would then appear to be outliers.

Immediate Interpretations — The horizontal line of the median between the two quartiles divides the box plot into an upper and lower half. If the two halves have about the same size, the distribution is symmetrical around the central index. A substantial asymmetry in the box will promptly indicate that the distribution is not Gaussian.

The “top-heavy” asymmetry of the box in Figure 5.2 immediately shows that the distribution is skewed right (toward high values). Because the mean and median have the same location in a Gaussian distribution, the higher value of the mean here is consistent with the right skew. In most distributions, the mean is inside the box; and a location beyond the box will denote a particularly egregious skew.

Figure 1-1

Degree of emphasis on the nurse as a sex object in mo­tion pictures, 1930-1980 (N = 211). (From Kalisch, B. J., Kalisch, P. A., & McHugh, M. L. [1982]. Research in Nursing and Health, 5, 150.)

 

Figure 1-2

Claimed region of ethnic origin (TV = 645). (From Clinton, J. [1982]. The development of an empirical construct for cross-cultural health research. Western Journal of Nursing Research, 4, 281.)

Figure 1-3

Subject and interviewer ratings of physical health of the older bereaved. (From Valanis, B. G, & Yeaworth, R. [1982]. Ratings of physical and mental health in the older bereaved. Research in Nursing and Health, 5, 142.)

 

 

Figure i-4

Illustration of the importance of the number of bars in designing a histogram for a set of data.

 

 

Figure 1-5

Number of previous births in a sample of women having cesarean deliveries (TV = 123). Data collected in program grant funded by National Center for Nursing Research, PO1-NR1859. PI., D. Brooten: Early Hospital Discharge and Nurse Specialist Followup.

 

 

 

 

Figure 1-6

Histogram of age in a sample of hysterec­tomy patients from an urban medical center (N = 112). Data collected in pro­gram grant funded by National Center for Nursing Research, PO1-NR1859. PI., D. Brooten: Early Hospital Discharge and Nurse Specialist Followup.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1-7

Illustration of the importance of the graph’s height in designing a histogram for a set of data. Data collected in program grant funded by National Center for Nursing Research, PO1-NR1859. P.I., D. Brooten: Early Hospital Discbarge and Nurse Specialist Followup.

 

Figure 1-8

Polygon superimposed on histo­gram shown in Figure 1-6. The two shaded triangles are congruent. Data collected in pro­gram grant funded by National Center for Nursing Research, PO1-NR1859. P.I., D. Brooten: Early Hospital Discharge and Nurse Specialist Followup.

 

 

Figure 1-9

Comparison of depression scores for patients having surgical procedure X (N = 104) and surgical procedure Y (N = 61). (Hypothetical data)

 

Figure 1-10

Example of histogram produced by SPSS: Denial scores from a sample of 152 heart at­tack patients. Qacobsen, B. S., & Lowery, B. J. [1992]. Further analysis of the psychometric properties of the Levihe Denial of Illness Scale. Psychosomatic Medicine, 54, 372-381.)

Figure 1-11

Histogram for psychological adjustment to illness by 195 patients with breast cancer (higher scores indicate poorer adjustment). (Lowery, B. J., Jacobsen, B. S., & Ducette, J. [1992]. Causal attribution, control, and adjustment to breast cancer. Psychosocial Oncology.)

 

Figure 1-12

Responses by 195 breast can­cer patients to the question of whether attitude will help to prevent a recurrence of cancer. Data collected in grant funded by National Center for Nursing Research, RO1-NR01897. P.I., B. J. Lowery. At tributions, control, and adjustment to breast cancer.

 

First-order degradation of pesticide residues can be described by the regression equation: log y = log a – (log b) x (y = residue, x = time). Conversion of the regression equation into antilogarithms yields the exponential function y= a/bx. As the results of residue analyses are subject to errors, the straight line that best fits the measured values must be computed by regression analysis. These computations and the graphic representation of the straight line and of the degradation curve back transformed into a linear coordinate system are performed with a desk top computer with plotter. Besides the constants log a and log b with their confidence intervals, the following parameters are computed: 1. Coefficient of determination (r2) as a measure of the dependence of the (logarithm of) residue on time; 2. Test quantity (D) which indicates whether or not such dependence exists; 3. Degradation times (T/X) with confidence interval; 4. Residue at a certain point of time (e.g. safety interval) with confidence interval; 5. Point of time at which a certain residue level is reached; 6. Outlier test, if necessary. The mathematical principles for the computation of these parameters are described.

            Graphical Representation of Data

The graphical representation of data makes the reading more interesting, less time-consuming and easily understandable. The disadvantage of graphical presentation is that it lacks details and is less accurate. In our study, we have the following graphs: 1. Bar Graphs 2. Pie Charts 3. Frequency Polygon 4. Histogram.

Bar Graphs

This is the simplest type of graphical presentation of data. The following types of bar graphs are possible: (a) Simple bar graph (b) Double bar graph (c) Divided bar graph.

Pie Graph or Pie Chart.

Sometimes a circle is used to represent a given data. The various parts of it are proportionally represented by sectors of the circle. Then the graph is called a Pie Graph or Pie Chart.

Frequency Polygon

In a frequency distribution, the mid-value of each class is obtained. Then on the graph paper, the frequency is plotted against the corresponding mid-value. These points are joined by straight lines. These straight lines may be extended in both directions to meet the X – axis to form a polygon.

Relative frequencies of class intervals also can be shown in a frequency polygon. In this chart, the frequency of each class is indicated by points or dots drawn at the midpoints of each class interval. Those points are then connected by straight lines. Comparing the frequency polygon (shown in Figure 1) to the frequency histogram (refer to Figure 1 in “Frequency Histogram”), you see that the major difference is that points replace the bars.

Whether to use bar charts or histograms depends on the data. For example, you may have categorical (or qualitative) data—numerical information about categories that vary significantly in kind. Gender (male or female), types of automobile owned (sedan, sports car, pickup truck, van, and so forth), and religious affiliations (Christian, Jewish, Muslim, and so forth) are all qualitative data. On the other hand, quantitative data can be measured in amounts: age in years, annual salaries, inches of rainfall. Typically, qualitative data are better displayed in bar charts; quantitative data, in histograms.

Histogram

A two dimensional frequency density diagram is called a histogram. A histogram is a diagram which represents the class interval and frequency in the form of a rectangle.

In a simple bar graph, the height of each bar represents the frequency. The thickness has no significance. All bars to have the same thickness.

We use double bar graph when we want to compare two things.

In the frequency polygon, the frequency is plotted against the mid value of each class. These points are joined by line segments.

 

 

The scientific methods of collection of data, its classification and application to commerce and everyday life is called statistics. A list of some important terms as follows: ungrouped data, tabulation of data, range, frequency, frequency distribution tally, inclusive type of grouped frequency distribution, exclusive type of grouped frequency distribution, lower limit and actual lower limit, upper limit and actual upper limit class size or class width class mark or class mid-interval. Variables, Continuous Variables (xv) Discrete Variables.

 

Graphical Representation

There are various methods of graphical representation of statistical data. In our study, we learn two types. Histogram Ogive or Cumulative Frequency Curve.

Cumulative Frequency

Cumulative frequency is obtained by adding the frequency of a class interval and the frequencies of the preceding intervals up to that class interval.

Frequency Curves

A histogram is a graphical representation of a frequency distribution in the form of rectangles with the class intervals as the bases and the corresponding frequencies as heights, without any gap between two successive rectangles. A polygon obtained by joining the mid-values of the widths of the consecutive rectangles of a histogram is called a frequency polygon. The formula to find the mid-value of a class interval is:

Thus, given a histogram, a frequency polygon can be drawn. A frequency polygon can be drawn even without drawing a histogram if the class intervals and their frequencies are known.

When the class intervals in a frequency distribution are decreased, the points of the frequency polygon come closer and closer and the frequency polygon tends to be a curve. If the class interval in a frequency distribution is very small, then the approximation of the frequency polygon is done by drawing it freehand in such a way that no corners remain in it and its area is approximately equal to the frequency polygon. The curve so formed is called a frequency curve. If the points corresponding to the ordered pairs are plotted on a graph sheet and joined by line segments, a frequency polygon is obtained. On the other hand, if the points are joined by a smooth curve, a frequency curve is obtained.

Cumulative Frequency Curve

A plot of the cumulative frequency against the upper class boundary with the points joined by line segments. Any continuous cumulative frequency curve, including a cumulative frequency polygon, is called an ogive. There are two ways of constructing an ogive or cumulative frequency curve. The curve is usually of shape.

A histogram is a diagram which represents the class interval and frequency in the form of a rectangle. The cumulative frequency curve is a shaped curve. Points on the cumulative frequency curve have abscissas as the actual upper / lower limits for ‘less than’ / more than curve and ordinates as the cumulative frequencies.

         GRAPHICAL REPRESENTATION OF DATA

Graphical representation is done of the data available this being a very important step of statistical analysis. We will be discussing the organization of data. The word ‘Data’ is plural for ‘datum’; datum means facts. Statistically the term is used for numerical facts such as measures of height, weight and scores on achievement and intelligence tests.

 

Tests, experiments and surveys in education and psychology provide us valuable data, mostly in the shape of numerical scores. For understanding data available and deriving meaning and useful conclusion, the data have to be organized or arranged in some systematic way. This can be done by following ways:

1. Statistical tables

2. Rank order

3. Frequency distribution

Statistical tables

The data are tabulated or arranged into rows and columns of different heading. Such tables can list original raw scores as well as the percentages, means, standard deviations and so on.

Rules for constructing tables:

1. Title of the table should be simple, concise and unambiguous. As a rule, it should appear on the table.

2. The table should be suitably divided into columns and rows according to the nature of data and purpose. These columns and rows should be arranged in a logical order to facilitate comparison.

3. The heading of each columns or row should be as brief as possible. Two or more columns or rows with similar headings may be grouped under a common heading to avoid repetition and we may have subheadings or captions.

4. Sub total for each separate classification and a general total for all combined classes are to be given. These totals should be given at the bottom or right of the concerned items.

5. The units in which the data are given must invariably be mentioned.

6. Necessary footnotes should be providing essential explanation of the points to ambiguous representation of the tabulated data must be given at the bottom of the table.

7. The sources from where the data have been received should be given at the end of the table.

8. In tabulating long columns of figures, space should be left after every five or ten rows.

9. If the numbers tabulated have more than three significant figures, the digit should be grouped in threes. For ex.- 4394756 as 4 394 756.

10. For all purposes and by all means, the table should be as simple as possible so that it may be studied by the readers with minimum possible strain and create a clear picture and interpretations of the data.

Rank order

The original raw scores can be arranged in an ascending or a descending series exhibiting an order with respect to the rank or merit position of the individual. Example:

Sixteen students of BA final psychology class obtained the following scores on an achievement test. Tabulating the given data –

5 8 4 12 15 17 18 12 20 7 8 19 6 9 10 11

S. No. Scores S No. Scores S No. Scores S No. Scores

1 20 5 15 9 10 13 7

2 19 6 12 10 9 14 6

3 18 7 12 11 8 15 5

4 17 8 11 12 8 16 4

Frequency Distribution

The organization of the data according to rank order does not help us to summarize a series of raw scores. It also does not tell us the frequency of the raw scores. In frequency distribution we group the data into an arbitrarily chosen groups or classes. It is also seen that how many times a particular score or group of scores occurs in the given data. This is known as the frequency distribution of numerical data.

 

Construction of Frequency distribution table

Finding the range:

First of all the range of the series to be grouped is found. it is done by subtracting the lowest score from the highest. In the present problem the range of the distribution is 46-12, 34.

Determining class interval:

After finding range we find class interval represented by Y. The formula for this is:

Writing the contents of the frequency distribution table:

Writing the classes of the distribution.

In the first column we write the classes of distribution. First of all the lowest class is settled and afterwards other subsequent classes are written down. In this case we take 10-14 as the lowest class, then wee have higher classes as 15-19, 20-24,.. and so on up to 45-49.

Tallying the scores into proper classes.

The scores given are tallied into proper classes in the second column then the tallies are counted against each class to obtain the frequency of the class.

 

GRAPHICAL REPRESENTATION OF DATA

The statistical data may be presented in a more attractive form appealing to the eye with the help of some graphic aids, i.e. Pictures and graphs. Such presentation carries a lot of communication power. A mere glimpse of thee picture and graphs may enable the viewer to have an immediate and meaningful grasp of the large amount of data.

Ungrouped data may be represented through a bar diagram, pie diagram, pictograph and line graph.

Bar graph represents the data on the graph paper in the form of vertical or horizontal bars.

· In a pie diagram, the data is represented by a circle of 360degrees into parts, each representing the amount of data converted into angles. The total frequency value is equated to 360 degrees and then the angle corresponding to component parts are calculated.

· In pictograms, the data is represented by means of picture figures appropriately designed in proportion to the numerical data.

· Line graphs represent the data concerning one variable on the horizontal and other variable on the vertical axis of the graph paper.

Grouped data may be represented graphically by histogram, frequency polygon, cumulative frequency graph and cumulative frequency percentage curve or ogive.

 

· A histogram is essentially a bar graph of a frequency distribution. The actual class limits plotted on the x-axis represents the width of various bars and respective frequencies of these class intervals represent the height of these bars.

 

· A frequency polygon is a line graph for the graphical representation of frequency distribution.

 

· A cumulative frequency graph represents the cumulative frequency distribution by plotting actual upper limits of the class intervals on the x axis and the respective cumulative frequencies of these class intervals on the y axis.

 

· Cumulative frequency percentage curve or ogive represents cumulative percentage frequency distribution by plotting upper limits of the class intervals on the x axis and the respective cumulative percentage frequencies of these class intervals on the y axis.

 

METHOD FOR CONSTRUCTING

A HISTOGRAM

1. The scores in the form of actual class limits as 19.5-24.5, 24.5-29.5 and so on are taken as examples in the construction of a histogram rather than written class limits as 20-24, 25-30.

2. It is customary to take two extra intervals of classes one below and above the grouped intervals.

3. Now we take the actual lower limits of all the class intervals and try to plot them on the x axis. The lower limit of the lowest class interval is taken at the intersecting point of x axis and y axis.

4. Frequencies of the distribution are plotted on the y axis.

5. Each class interval with its specific frequency is represented by separate rectangle. The base of each rectangle is the width of the class interval. And the height is representative of the frequency of that class or interval.

6. Care should be taken to select the appropriate units of representation along the x and y axis. Both the axis and the y axis must not be too short or too long.

 

METHOD FOR CONSTRUTING

A FREQUENCY POLYGON

1. As in histogram two extra class interval is taken, one above and other below the given class interval.

2. The mid-points of the class interval is calculated.

3. The mid point is calculated along the x axis and the corresponding frequencies are plotted along the y axis.

4. The various points given by the plotting are joined by lines to give frequency polygon.

DIFFERENCE BETWEEN HISTOGRAM AND FRQUENCY POLYGON

Histogram is a bar graph while frequency polygon is a line graph. Frequency polygon is more useful and practical. In frequency polygon it is easy to know the trends of the distribution; we are unable to do so in histogram. Histogram gives a very clear and accurate picture of the relative proportion of the frequency from interval to interval.

METHOD FOR CONSTRUTING

A CUMULATIVE FREQUENCY GRAPH

1. First of all we calculate the actual upper and lower limits of the class intervals i.e. if the class interval is 20-24 then upper limit is 24.5 and the lower limit is 19.5.

2. We must know select a suitable scale as per the range of the class interval and plot the actual upper limits on the x axis and the respective cumulative frequency on y axis.

3. All the plotted points are then joined by successive straight lines resulting a line graph.

4. To plot the origin of the x axis an extra class interval is taken with cumulative frequency zero is taken.

         Statistics is that branch of mathematics devoted to the collection, compilation, display, and interpretation of numerical data. In general, the field can be divided into two major subgroups, descriptive statistics and inferential statistics. The former subject deals primarily with the accumulation and presentation of numerical data, while the latter focuses on predictions that can be made based on those data.

Perhaps the simplest way to report the results of the study described above is to make a table. The advantage of constructing a table of data is that a reader can get a general idea about the findings of the study in a brief glance.

Two fundamental concepts used in statistical analysis are population and sample. The term population refers to a complete set of individuals, objects, or events that belong to some category. For example, all of the players who are employed by Major League Baseball teams make up the population of professional major league baseball players. The term sample refers to some subset of a population.

Statistics – Collecting Data

Statistics – Graphical Representation

The table shown above is one way of representing the frequency distribution of a sample or population. A frequency distribution is any method for summarizing data that shows the number of individuals or individual cases present in each given interval of measurement. In the table above, there are 5,382,025 female African-Americans in the age group 0-19; 2,982,305 in the age group 20-29; 2,587,550 and…

Statistics – Distribution Curves

Finally, think of a histogram in which the vertical bars are very narrow…and then very, very narrow. As one connects the midpoints of these bars, the frequency polygon begins to look like a smooth curve, perhaps like a high, smoothly shaped hill. A curve of this kind is known as a distribution curve. Probably the most familiar kind of distribution curve is one with a peak in the middle.

Statistics

Other Kinds Of Frequency Distributions

Bar graphs look very much like histograms except that gaps are left between adjacent bars. This difference is based on the fact that bar graphs are usually used to represent discrete data and the space between bars is a reminder of the discrete character of the data represented. Line graphs can also be used to represent continuous data. If one were to record the temperature once an hour all day to week.

Statistics – Measures Of Central Tendency

Both statisticians and non-statisticians talk about “averages” all the time. But the term average can have a number of different meanings. In the field of statistics, therefore, workers prefer to use the term “measure of central tendency” for the concept of an “average.” One way to understand how various measures of central tendency.

Measures Of Variability

Suppose that a teacher gave the same test to two different classes and obtained the following results: Class 1: 80%, 80%, 80%, 80%, 80% Class 2: 60%, 70%, 80%, 90%, 100% If you calculate the mean for both sets of scores, you get the same answer: 80%. But the collection of scores from which this mean was obtained was very different in the two cases. The way that statisticians have of distinguishing…

Statistics – Inferential Statistics

Expressing a collection of data in some useful form, as described above, is often only the first step in a statistician’s work. The next step will be to decide what conclusions, predictions, and other statements, if any, can be made based on those data. A number of sophisticated mathematical techniques have now been developed to make these judgments. An important fundamental concept used in biostatistics.

 

Computer forensics is the preservation, analysis, and interpretation of computer data. There is a need for software that aids investigators in locating data on hard drives left by persons committing illegal activities. These software tools should reduce the tedious efforts of forensic examiners, especially when searching large hard drives. A method is proposed here that uses visualization techniques to represent file statistics, such as file size, last access date, creation date, last modification date, owner, and file type. The user interface to this software allows file searching, pattern matching, and display of file contents. By viewing file information graphically, the developed software will reduce the examiner’s analysis time and greatly increase the probability of locating criminal evidence.

Computer forensics is the preservation, analysis, and interpretation of computer data. In a world wherein the number of crimes committed using computers is increasing rapidly, a definite need exists for forensic software tools. These tools allow investigators to follow digital tracks left by persons committing illegal activities. Traces of evidence may be found in plain text documents, log files, or even system files, yet more technologically advanced criminals may conceal information by deleting it, encrypting it, or embedding it inside another file. With the large amount of storage space available on modern hard drives, searching for a single file becomes quite tedious without the help of special forensic tools. Using visualization techniques to display information about computer data can help forensic specialists direct their search to suspicious files.

A great deal of time is wasted trying to interpret mass amounts of data that is not correlated or meaningful without high levels of patience and tolerance for error. A well quoted phrase, “a picture is worth a thousand words,” is what we’re trying to accomplish here. Human brains have the ability to interpret and comprehend pictures, video, and charts much faster than reading a description of the same. This is because the human mind is able to examine graphics in parallel but only examine text in serial. Imagine a friend trying to describe in an email the beauty of the Shenandoah Valley using the best vocabulary he has. It takes some time because there are so many elements to convey without misrepresenting the Shenandoah Valley as another valley full of green trees. Eventually, the friend decides it is best just to show a picture taken from a scenic overlook. You are amazed at the beauty and realize it would have taken thousands of words to describe it all.

One single picture not only presented an accurate representation of the Shenandoah Valley but saved you reading a very long email. Using this concept of visual perception, we have developed a graphical user interface (GUI) that displays file information visually. The user is able to query a specific directory to query and see statistics, such as file size, access date, creation date, modification date, owner, and file type, represented by pixel intensity or colour, wherein each pixel represents a file.

Requests for more information about a suspect file can be filled by clicking on the display and walking through various menus. Viewing information about multiple files or understanding the relationship between them is also helpful. The user interface to this software allows file searching, pattern matching, and display of file contents. Each of these options allows a deeper analysis of the data stored on the hard drive and results in a flexible and customizable tool for locating criminal evidence.

The software tool we have developed will greatly aid the computer forensic process by reducing the time to identify suspicious files and increasing the probability of locating criminal evidence. This is done by using a graphical representation of the file rather than traditional text.

Our contributions to computer science include the use of enhanced tree-maps, applied visualization techniques for computer forensics, and a software framework on which to build future enhancements. Enhanced tree-maps help represent temporal information about files, such as access time. Traditional tree-maps only have the capability of representing spatial information, such as size. The first to apply visualization techniques to computer forensics and will show it to be a promising method for identifying hidden or altered files. Lastly, our software allows for additional visualization techniques not yet developed.

Documentation

During the analysis process, detailed information must be recorded if there is to be any hope of a successful court appearance. This information includes forensic tools used, actions taken, and chain of custody. Some forensic tools have more credibility in court than others because they have been proven. Thus, it is important to use a proven forensic tool. Actions taken include opening files and hashing. Time of day should be recorded whenever a file is opened, hashed, or scanned, along with the directory it was discovered in. Every examiner involved in the case needs to be recorded in the chain of custody. At any time in the investigation, it should be clear and possible to identify the individual who carried out an analysis task.

Court Appearance

Once the evidence has been analyzed, authenticated, and documented, it may go to court. It is important to present the case in a simple and clear manner because judges and juries may not have technical knowledge of computer systems. Investigators who have followed the forensic process will have a higher probability of winning the case. However, if there are holes in the chain of custody or any step of the forensic process, the defence will exploit them and usually succeed at convincing the jury the investigation was handled improperly.

The prosecution, thus, would not be able to rebuild their case and would loose. An understanding of the computer forensic process leads to the development of improved software that aids investigators in locating evidence. Any software used to collect or

analyze evidence must follow the computer forensic guidelines; otherwise, its use becomes a hindrance rather than a benefit.

Visualization of Data

Tree-Maps

In our method, we use visualization techniques to help represent file attributes. One method of displaying the relationship of files visually in two dimensions is called a tree map. Schneiderman describes tree-maps as 2D space-filling algorithm for complex tree

structures. They are designed to display the entire tree structure in one screen. Each file is represented by a shaded box that adheres to a chosen colouring scheme that highlights file and directory boundaries. Box size is determined by two parameters: the size of the user selected display region and percentage of the selected directory the file occupies. Other file directory representations like that of Windows Explorer use nodes and edges rotated on their side and always require scrolling up and down to view the complex structure.

The tree-map facilitates easy recognition of the largest files because they take up the most space in the 2D display. The method of using tree-maps to visualize data storage and directory structure greatly reduces the time it takes to locate large files in a tree structure that is nine levels deep and contains many thousands of files. Tree-maps are primarily designed to emphasize large files. However, Schneiderman does point out that a user can drag a mouse over the display and click on a shaded box to query the system for the file name or other information. Such additions may enhance the usefulness of tree-maps, but stand-alone tree-maps for computer forensics contain many weaknesses. Small files and directories are hidden among larger files and may not even show

up on the display. We may be looking for a simple file on a massive hard drive. If the file is small or if the disk contains numerous files, our file will hardly stand out.

For our purposes, stand-alone tree-maps require enhancement that provides the user with advanced filtering and display techniques. In this way, tree-maps are interesting and provide groundwork for opportunities in computer forensics

“Graphic representation of statistics” Videos

Graphic representation of statistics Questions & Answers

Question: Name the different graphical representation of data use in statistics

Answer: graphical representation of statistical data is for the sole purpose of easier interpretation. in modern manufacturing it has been converted to ‘statistical process control’ which sprung the ‘seven QC tools’ and was recently upgraded the seven QC tools: flow charts run charts paretic diagram histogram cause effect diagrams scatter diagrams control chart (the most famous and widely used) the new version: affinity diagrams relations diagrams tree diagram matrix diagram arrow diagram process decision program charts matrix data analysis just type any of the key words i put in here in your search engines and you’ll have better explanations about them good luck

Question: Based on your observation list out 4 points on the characteristics of logarithmic or exponential functions and their graphical representation.

Answer: they are mirror images of each other. That’s one.

Question: Working with Numbers Number Operations and Number Sense Simple Algebra Algebra, Functions, and Patterns Geometry and Graphing Measurement, Geometry and Coordinate Geometry or lead me to a site. 4. Statistical Math Data analysis, reading graphical representations of data Statistics and probability

Answer: I’m not trying to just get points, but no one can help you with this. you have to have real problems, because these subjects are so broad that it would be impossible to cover these even simply without talking an hour.

In medical statistics themselves the following kinds of relative parameters are used:

– Extensive;

– Intensive;

– Relative intensity;

– Visualization ;

– Correlation.

For the determination of a structure of disease (mortality rate, lethality, etc.) the extensive parameter is used.

The extensive parameter or a parameter of distribution characterizes a parts of the phenomena (structure), that is it shows, what part from the general number of all diseases (died) is made with this or that disease which enters into total.

Using this parameter, it is possible to determine the structure of patients according to age, social status, etc. It is accepted to express this parameter in percentage, but it can be calculated and in parts per thousand case, when the part of the given disease is small and at the calculation in percentage it is expressed as decimal fraction, instead of an integer.

The general formula of its subtraction is the following:

Technique of the calculation of an extensive parameter will be shown on an example.

To determine an age structure of those who has addressed in a polyclinic if the following data is known:

Number of addressed – 1500 it is accepted by 100 %, number of patients of each age – accordingly for X, from here per cent of what have addressed in a polyclinic in the age of 15-19 years from the general number, will make:

 

1500– 100

150 – X,                 

 

Table 2.5. Age groups of people, which have visit to polyclinic

 

Conclusion: most of the people that have addressed in a polyclinic were in the age of 20-29 and 40-49 years.

The extensive parameter at the analysis needs to be used carefully and we must remember, that it is used only for the characteristic of structure of the phenomena in the given place and at present time. Comparison of a structure makes it possible to tell only about change of a serial number of the given diseases in structure of diseases.

If it is necessary to determine distribution of the phenomenon intensive parameters are used.

The intensive parameter characterizes frequency or distribution.

It shows, how frequently the given phenomenon occurs in the given environment.

For example, how frequently there is this or that disease among the population or how frequently people are dying from this or that disease.

To calculate the intensive parameter, it is necessary to know the population or the contingent.

General formula of the calculation is the following:

Intensive parameters are calculated on 1000 persons. These are parameters of birth, morbidity, mortality, etc.; on separate disease they are being calculated on 10.000 and disease, which occurs seldom – on 100000 persons.

Let’ s consider a technique of its subtraction on an example.

Example. Number of died in the area – 175, number of the population at the beginning of year – 24000, at the end of year – 26000. To determine a parameter of mortality:

 

We determine an average value of the population; for this purpose we take the number of the population to the beginning of year plus number of the population at the end of year and divide it by 2:

 

We make a proportion: 175 persons, who died correspond to 25000 people, and how many persons, who died correspond to 1000?

 

175-25000

ò – 1000

 

Parameters of birth, morbidity are calculated similarly etc.

Table 2.6. Structure of morbidity, invalidity and the reasons of mortality

 

Parameters of relative intensity represent a numerical ratio of two or several structures of the same elements of a set, which is studied.

They allow determining a degree of conformity (advantage or reduction) of similar attributes and are used as auxiliary reception; in those cases where it isn’t possible to receive direct intensive parameters or if it is necessary to measure a degree of a disproportion in structure of two or several close processes.

For example, there are data only about structure of the general morbidity, physical disability and mortality rate.

Comparison of these structures and subtraction of parameters of relative intensity allows finding out the relative importance of these or those diseases in health parameters of the population.

So, for example, comparison of densities of physical disability and mortality rates from cardiovascular diseases with its densities in morbidity allows to determine, that cardiovascular diseases occupy almost in 7 times more part in physical disability and almost in 5 times – in mortality, than in structure of morbidity.

Procedure of the calculation of these parameters is the following:

For example, densities of cardiovascular diseases in structures:

 – General morbidity              – 4,0 %;

– Disability                              – 27,0 %;

– Reasons of mortality                     – 19,0 %.

The parameter of relative intensity of disability is received by a division of densities of cardiovascular diseases in structure of disability to densities of these diseases in the structure of the general morbidity, which equals:

.

The parameter of relative intensity of mortality is received in the similar way:.

Thus, parameters of relative intensity represent parameters of a disproportion of particles of the same elements in the structure of processes, which are studying.

The parameter of visualization characterizes the relation between diverse values.

For example, the parameter of average bed occupancy, nurses, etc.

The techniques of subtraction of the visualization parameter is the same as for intensive parameter, nevertheless the number of an intensive parameter stands in the numerator, is included into denominator, where as in a parameter of visualization of numerator and denominator different.

Example. Number of beds – 280, an average number of the population – 260000. What is the bed occupancy (BO) rate?

 BO rate = on 10.000 persons.

The parameter of correlation characterizes the relation of any of comparable values to the initial level accepted for 100. This parameter is used for convenience of comparison, and also in case shows a direction of process (increase, reduction) not showing a level or the numbers of the phenomenon.

It can be used for the characteristic of dynamics of the phenomena, for comparison on separate territories, in different groups of the population, for the construction of graphic.

 Results of examinations after their statistical processing can given as graphic representations, on which numerical numbers are presented as drawing. Schedules give a general characteristic of the phenomenon and define its general laws, enable to analyze the given researches more deeply.

They facilitate comparison of parameters, give imagination about structure and character of connection between the phenomena, specify their tendencies.

Therefore, graphic demonstration we often connect with the graphic analysis for which the graphic representation serves not only means of demonstration of results and conclusions research, but also means of the analysis of the received materials, revealing of internal connections and laws.

At construction of schedules character of the data which are subject to a graphic representation, purpose of schedules (demonstration at conference, lectures, a reproduction in scientific work, etc.), the purpose of the schedule (evidently to show the received results or only to emphasize, allocate any law or the fact), a level of an audience before which the schedule is shown are taken into account.

The choice will depend on all it is the following as a graphic representation, color, the number, a proportion of a print, etc. In all cases schedules should be clear, convenient and easy for reading.

In medical statistical researches linear diagrams, plane diagrams, cartograms and linear or coordinate are used.

LINEAR DIAGRAMS are schedules on which numerical values are displayed by curves which allow to trace dynamics of the phenomenon in time or to find out dependence of one attribute on another.

Whether on linear diagrams with two and a plenty of curves probably also comparison of numbers in two the greater number of dynamic lines, and also an establishment of dependence of changes of fluctuations which occurs in the other number line.

Linear diagrams are made according to system of rectangular coordinates where the horizontal scale is postponed at the left – to the right on a line of abscissas (X), and vertical – from below – upwards on a line which is called as ordinate (Y). The obligatory requirement of construction of any schedule is scale, that is the image on drawing should be reduced, compared with corresponding figures.

Contrast to linear diagrams which describe dynamics of any process, plane diagrams are used in the case when it is necessary to represent the statistical phenomena or the facts, independent one from another.

The most simple example of plane diagrams is the diagram as rectangular or figures. Digital numbers on plane diagrams average represented by geometrical figures – rectangular, squares. These diagrams are used for demonstration and popularization of the resulted data, and also in cases if it is necessary to represent structure of the phenomenon on one of the moments of supervision.

For example, age type fallen ill or structure of disease in any settlement.

Fig. 2.2 Age structure of the population (the part of each age layer was determined to all population).

 

In long-pillar diagrams digital numbers are represented by rectangular columns with an identical basis and different height.

The height of a rectangular corresponds to the relative value of the phenomenon which is studied. For construction a long-pillar diagram we use a scale according to which it is possible to determine the height of each column.

Long-pillar diagrams serve for comparison of several sizes. It is possible to rectangular which represent sizes, it is possible to place also on the plane diagram not on a vertical, and across and then there will be a tape diagram (Fig.4). In some cases the image of sizes as tapes (stirs) is more convenient, than as columns because it is easier to sign with each tape by a horizontal inscription.

With the aid of column and tape diagrams it is possible not only to compare different sizes, but also simultaneously to display structure of these numbers and to compare their parts. For example, long-pillar or tape diagrams which show distribution of diseases on the basic nosological forms, it is possible to show also percent of diseases among men and women.

For this purpose it is necessary (a figure or a tape) to divide each rectangular for two parts, any of which will correspond to digital number of disease among men and women.

In circular diagrams they use to display ratio of homogeneous absolute sizes.

They don’t use the area of a rectangular, but the area of a circle.

But it is necessary to remember, that the areas of circles match up one another as squares of their radiuses, therefore at construction of circular diagrams we must extract off the diagram sizes and on this basis to construct radius, and having radius, it is easy to describe a circle.

In a case if the circular diagram displays parts of the whole, it is necessary to display circles not separately one from another, and to impose against each other. The whole is possible also and its parts to submit as the circle divided on sectors – the sector diagram. At construction of the sector diagram all area of a circle is accepted for 100 %, and each sector occupies is the following part of the area which correspond to the necessary percent.

In practice for construction of sector diagrams it is possible to use not only the area of a circle, but also the area of a square and a rectangular.

Nevertheless, often it happens to divide is the following figures is more hard, than a circle and consequently they are rather seldom used as a basis of sector diagrams.

Radial or linear – circular diagram (Fig.2.3) are constructed on the basis of number coordinates in which the radius replaces vertical scale of diagrams which are based on system of rectangular coordinates.

The example of the radial diagram is a wind rose with the aid of which we represent on maps the change of a direction of a wind during any calendar period of time (month, year).

Radial diagrams are used for an illustration of seasonal fluctuations of any numbers, for example diseases or mortality rates.

These diagrams are constructed on a circle which center has12 radiuses. Each radius saws from a circle an arch in 30 (360/12=30) also represents ordinate of one of calendar months: January, March, etc.

As an initial zero point they take the center of a circle, and then on radiuses according to the scale chosen before render numbers which display intensity of seasonal fluctuations of the phenomenon in any of calendar months.

Having connected the marked points, we receive the closed line which enables to imagine seasonal fluctuations.

When building radial diagrams, it is necessary to remember a rule of calculation of radiuses from the top part of the diagram and in other words.

Fig. 2.3 The radial diagram.

 

Comparisons of the different phenomena according to a territorial attribute cartograms are built, if necessary. They represent geographical maps, on which with the aid of graphic symbols where the intensity of distribution and grouping of the phenomenon ( morbidity, mortality, etc.) for any period of time ( Fig. 2.4) is shown.

Therefore they are better for building on simplified maps on which only administrative frontiers and some big settlements are shown. At construction of a cartogram the great value has grouping the phenomena which are displayed.

The most simple grouping is division of some parameters on group with parameters below average and group with parameters is higher than average. According to this division regions districts with parameters than will be shaded on a cartogram and below average – not shaded.