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* Definition

* Operationalization of variables

* Population and sample

* Techniques and Tools for Data Collection

* Graphics

* Definition.

These are attributes, qualities, observable characteristics possessed by people, objects, institutions expressing varying magnitudes discretely or continuously. Example: people are variables: age, sex, height, weight, build, hair color, eye color, degree of attention, prior knowledge, faith, origin, social class, etc..

Variables are things, objects: shape, color, size, weight, maintenance, service, etc.. Institutions also have variables such as age, organization, efficiency, size, productivity, etc..

2. Rating: There are various classifications of variables.

2.1. By their degree of abstraction or concreteness.

a.Variables Theory: Are those that are abstract not understand because they are not observable or measurable but defined. Examples: socioeconomic status, academic performance, imperialism, dependency, domination, infrastructure.

b.Variables Intermediate: Those that provide insights into the theoretical variables. Example Academic performance is not understood but is referred to the descriptions, care, dedication to the study, student punctuality.

c. Empirical variables: indicators are those that allow us to understand better the intermediate variables and therefore the theoretical variables. No need to be defined because they are easily understandable, measurable or observable. Examples: qualifying the variable can be very good, good, fair, poor and very poor. The empirical variables can be expressed quantitatively.

2.2. Given its position in the investigation:

a. Dependent Variable: That which in the result represents a hypothesis, the effect, the phenomenon being studied. It is symbolized by the letter Y. Example: between academic variables and application of methods, the dependent variable is academic achievement. In a typical mathematical function as: Y = (f) X (read and is a function of X, or Y depends on X)

b. Independent Variable: This is one that influences the dependent variable and not dependent on another variable in a hypothesis. It is symbolized by the letter X. Example: variables between hyperactivity and lack of self-esteem, self-esteem is an independent variable, as it explains or influences the child’s hyperactivity.

c. Variable Strange: External are those that come from outside the field of research and therefore are also called intervening. They are of various kinds but what interests us is related variables, or variables subject and organic, as are the qualities of the subject under investigation eg, age, sex, intelligence, prior knowledge, origin, etc.. and which can influence the dependent variable, for example achievement. In other extraneous variables hypothesis may come from outside the subject of study. Are symbolized with the letter Z. (Sierra, 1988:142).

2.2.Por their nature: They can be qualitative and quantitative ordinal. (Chavesta Fernandez Brothers, 1993:15)

a. Qualitative Variables: those who nominate or indicate qualities. Example: The variable size can be expressed: very high, high, medium, low, very low.

b. Ordinal variables are expressing a hierarchical classification, in order of importance. Example: the variable level of instruction includes: illiterate, primary, secondary, tertiary.

c. Quantitative Variables: be discrete and continuous

c.1. Discrete Variables: are integers expressing therefore may be counted. Example school population, oil production, birth, death, etc..

c.2. Continuous variables are those which expressed in decimal numbers therefore can be measured more accurately. Example: the weight, size or age of a person.Operationalization of variables:

This operation is to transform the theoretical variables and intermediate variables then empirical variables or indicators.

From this table it can be inferred that the theoretical variable “socioeconomic status” is defined as the economic, social, political and cultural that has a person in society, characterized by both intermediate variables such as income, social class, educational level and political relations. These intermediate variables can be observed and measured if they become empirical variables or indicators such as those shown in each case.


According thesis:

“Analysis of the causes that have led to tax evasion in the Main Maritime Customs Guaira in the period 2005-2006)


The population is the set of all cases that match a set of specifications, we can say that the population is the whole phenomenon to study, where the population units have a common feature which gives rise to studies and data. (Hernandez Sampieri and others, 2000)

For this research, people will turn away a group (108 subjects) for the areas and / or divisions needed taken as reference of the Main Customs of La Guaira. These represent 100% of the same. As can be evidenced in Table 1.

Box 1. Determination of Population

Source: A. Andara, J. Carreo 2001, collected in the Human Resources Department of the Main Customs of La Guaira.

Graph 1. Selected Population


The sample is defined as a subset of the population. To define the characteristics of the population. (Hernandez Sampieri and others, 2000)

According to Acevedo (1984) defines the show as “a population that is, a number of individuals, an object of which is an element of the universe or population, ie, a set of the population that are working” at which this research is limited to the number of cases that are handled in the Main Customs of La Guaira.

Table 2. Sample Identification

Source: A. Andara, J. Carreo 2001. Main Customs of La Guaira.

Chart 2. Sample Identification

Techniques and Tools for Data Collection


The technique according to the Libertador Experimental Pedagogical University (1998) defines it as the answers on how to do specific operating procedures to be followed through the different phases of the method. The techniques are practical and operational and the method is global and coordination of operations.

The data collection techniques are the strategies used by the researcher to gather information about an event or phenomenon. These vary according to the type of research include: surveys, observation, document analysis, among others … The instruments are the means for the implementation of the research strategy to follow, can be presented in formats, videos, photographs, etcetera. The techniques used for this research were the interview and content analysis.

The interview is a conversation between the interviewee and the interviewer, to first obtain the necessary information to gather enough data to tabulate and analyze. This Sabino C. (2002), defines the interview as:

A specific form of social interaction that aims to collect data for research. The investigator asks questions to people capable of offering interesting information, establishing a dialogue peculiar, asymmetric, where one party seeks to collect information and the other is the source of this information … “(p. 106)

Moreover we used content analysis is a technique that analyzes and reports written work previously performed and are taken as reference. (Sanchez, 1998, p. 68).


They constitute natural means through which it is possible to obtain and file the information required for the investigation. (Hernandez Sampieri and others, 2002)

In this work were used as instruments in the first questionnaire, which is very common and often used for field investigations, formulating Ten (10) closed type questions, for it (Ruiz, 1998, cited in the Handbook The elaboration of the Special Degree), defines it as: “A data collection instrument, paper and pencil, composed of a set of questions seeking information related to a problem, subject or research topic, which is administered to a group of people. ” (P.33)

Another instrument used in the research was the report, written work already performed, which allowed sustain and support the study conducted in the Main Maritime Customs Guaira, for it believes Ramirez about:

The review of existing literature on the subject will reveal the status of the area of our interest (how many and what studies have been done, theoretical and methodological approaches, results, etc.), besides giving us the theoretical elements that will help us better understand the research question posed. How to do it.

To obtain the necessary information, was used as library materials: reports, written work previously performed and texts and laws.


Much of the utility of descriptive statistics is to provide a means to report based on the data collected. How effectively can make such reporting process upon presentation of the data, the graphics being one of the fastest and most efficient, but also one of the most to be manipulated or misinterpreted if precautions are not taken to perform basic graphics. There are also several types of charts, or graphics, using each of them according to the type of information that is being used and the objectives sought to present the information.

Then mention some considerations to be taken into account when making any graph so that the information is transmitted as efficiently as possible and without distortions:

* The axis representing the frequency of observations (commonly vertical or ordinate) should start at zero (0), otherwise it could give wrong impressions to compare the height, length or position of the columns, bars or lines representing frequencies.

* The length of the spaces representing each data or interval (class) in the graph must be equal.

* The graph type must match their characteristics with the type of information or the objective pursued by representing, otherwise the plot becomes an ineffective tool, which produces more confusion than anything else, unnecessary misunderstandings or producer . For example, if you want to represent the proportion of male population in a country is best for using a pie chart or circular bar graphs to compare it against the female population on the one hand it can be seen that proportion is seen by the other Which of the two populations is greater.

There is a point worth note: there is software that enables the rapid and efficient construction of graphs from databases or spreadsheets, but no matter how cute, well delineated, dyed or made is a graph, if not have taken into account such considerations having to do more about the purpose of these tools and Statistics: the efficient transmission of information.

Chart Types

Frequency distributions for the most common plot is the histogram. An example is presented below, which represents the number of “hits” that has had this hypertext according to the time of the visit.

On the horizontal axis (or abscissa) are plotted data intervals, marking continuously boundaries between each of these. Thus, the histogram comprises rectangles, whose number corresponds with the number of intervals considered, the width of the base of each of these rectangles is the same and always coincide with the boundaries of the intervals, and the height corresponds to the frequency of each interval.

It is important to note that it is difficult to use this type of representation when there are open intervals or when the intervals are not equal.

The Excel program not automatically creates histograms thus provides the width of the columns so that become separated. However, there is a way to make them.

A chart type is very similar to the graphical histogram columns. For this type of graph, made from rectangles also requested that their bases are the same width and height equivalent to the frequencies. For this type, unlike the histogram, it is not necessary to have a continuous horizontal scale, so that rectangles (or bars) does not have to occur close together.

Another relevant observation is that can be represented in the same graph, using the same horizontal and vertical scales, multiple data for the same variables product of several observations. This produces a graph with multiple sets, each corresponding to each observation of the sample (or population), and taking a graph composed. Ideally, each set of data (or observations) are illustrated or illuminated equally with each other, but different from the others.

The following example belongs to the behavior of the three partial grades school students. The series (each partial qualifications) are colored with different colors to show the behavior individually, as each of the students with respect to others. Interestingly, the horizontal scale is not continuous (is nominal).

It is possible, and if resources permit, to render graphics compounds in a “three-dimensional”, ie, with graphics that have not only two axes, but three, and where rectangles are replaced by rectangular prisms (occasionally market software allows use prisms are polygons whose regular basis over four sides, pyramids or cylinders). An example is the following:

Which represents the percentage of GDP spent on education and research for five countries in the period from 1988 to 1999 (source: “Science and Development”, 1994, XIX (114): 12). It is important to consider that this type of graphics can get very complicated, making information less readable.

It is also possible to make horizontal bar charts, which are very similar to column graphs, with the important caveat that the function of the axes is exchanged and the horizontal axis is aimed at the frequencies and the vertical axis to classes.

It is very common that this kind of graphics are used to illustrate the size of a population divided into layers, for example, are their ages. The example given is the population of a fictitious country called “Timbuctulandia”:

In this particular chart type is called age pyramid in shape. Even when comparing male and female population by age strata, the style uses the left for the people of one sex and the right side to the other, the result is a “pyramid” almost symmetric (depends on the population particular).

When data are interrelated, that is, when we say that there is some continuity between observations (such as population growth, the evolution of the weight and height of a person over time, the academic performance of a student along its schooling, variations in the measurement on a per second or minute experiment) can use the graphs of lines which consist of a set of plotted points at intersections and classmark frequencies each, with lines joining successively:

This example shows the behavior of the body weight (in kilograms) of two individuals over five annual observations. As in the case of the column graphs (and others) can present several series of observations (in this case each series of observations are the weights of the individual).

Another way of representing a less common, and very similar to line graphs, is the frequency polygon. The fundamental difference between them is that in the frequency polygon adds two classes with zero frequencies: one before the first class and other data after the last. The result is that the “subject” line at both ends and the horizontal axis could be an axis line becomes separated, along with it, in a polygon.

The example below shows the percentage of GDP spent on teaching and research during 1990 in five countries (source: “Science and Development”, 1994, XIX (114): 12):

Excel does not automatically create the frequency polygons, but produces line graphs. However, it is possible to manage them.

A graph similar to the line frequency is the warhead, but it is partially obtained by applying the same technique to a cumulative distribution and just as these, there older warheads and minor ogives.

There are two fundamental differences between warheads and frequency polygons (and therefore the application of the technique is partial):

* One end of the ogive is not “tied” to the horizontal axis, for greater warhead case with the left end, to the ogive less than, to the right.

* On the horizontal axis instead of placing the class marks are placed class boundaries. In the case of the warhead is greater than the lower boundary, for the warhead smaller than the largest.

The following are examples of warheads left the greater than, the lowest right which, using data which were used to exemplify the histogram:

The warhead greater than (left) is called this because seeing the point that is on the border class “4:00” are visits that were made in a time greater than 4:00 pm (in temporal matters would say: after 4:00 pm). Similarly, on the shoulder lower than the frequency that is represented in each class border are the number of observations less than the indicated border (where time is the number of observations before the time that marks the border).

When using a cumulative distribution percentage is then obtained a warhead (greater than or less than as applicable) whose vertical axis has a scale of 0% to 100%. The following example is the same warhead smaller than that just used, but with a percentage distribution:

At times, when comparing two sets of observations (or data) call using a graphical areas, which is filled the area that is below the lines resulting from a line graph.

The example presented is the comparison of the total species of the order Carnivora families and those in danger in Mexico (source: “Science and Development”, 1994, XIX (114): 58):

When what you want is to highlight some subsets representing proportions in the total, ie when using a categorical scale, should use a pie chart or circular call.

For example, to illustrate the undergraduate enrollment (in Mexico) by knowledge area in the year 1992 you can use something like follows (Source: ANUIES, 1995):

In fact, if you want to highlight one of the categories presented, is valid to take this “slice” of the graph and separate it from the others:

You have to take some precautions when using this type of graphics. First, compare two pie charts (for example, if you wanted to compare the proportion of undergraduate enrollment by field of knowledge in BA for two different years) is very difficult and therefore not very desirable.

Furthermore, occasionally there are categories with few frequencies (eg two or three with relative frequencies below 1% each), making the resulting graph “heavy” and encimen labels. One possible solution is to put them together in a single category (eg, the typical “other” or “many”), but then would have to weigh if a extra graphics such observations only, with the relevant entry or simply ignored by no meaningful result.

Currently, much in the mass media, graphics are used to illustrate the data or the results of any investigation. Regularly drawings are used to represent such information, and the size or number of these drawings within a graphic is determined by the corresponding frequency. This type of graph is called pictogram and here are two examples:

The left represents the population of the United States (each man represents two million inhabitants), on the right represents the mass of three planets in our solar system as the unit to the mass of the Earth (each represents the mass of our planet: Venus and Neptune have smaller mass is over 17 times more mass than Earth).

Excel versions 7.0 and earlier do not have options for this type of graphs, the post itself. Other contemporary programs (such as Corel Draw or Harvard Graphics) they are capable.

When we seek to illustrate the dispersion of the observations, and some things work well as correlations can use a scatter plot. For example, the example on the left is the dispersion that occurs when comparing the number of doctoral theses in sciences against the total number of doctoral theses (particularly in Mexico) in annual observations between 1984 and 1990 (source: “Science and Development “, 1994, XIX (114): 12):

The graph on the right is the result of comparing the diameter (in thousands of kilometers) of the inner planets of our solar system against their densities (in grams per cubic centimeter). Interestingly, the points seem to “follow” an imaginary line that resembles a line, with the exception of an outlier: Mercury.

One use of this kind of plot is precisely find if the observations follow a linear pattern (a trend line) or if there are outliers. In the case of Excel, the program is capable of plotting trend lines that follow a set of data.

A similar type of graph charts are graphs of dispersion of bubbles, which are present in the dispersion of the observations in the same way as those, but it adds the ability to display another variable represented in the dot size, as these become circles (bubbles) with radii proportional to the magnitudes which represent.

This example compares the distance in each of the inner planets of our solar system to the Sun against the time needed to traverse their orbits, and the size of the bubbles indicates the mass of each planet.

There are also other types of plots, each with unique characteristics that provide certain intention for use, such as radar charts and polar plots.