The** tables and graphs** They are analysis tools, whose purpose is to organize, summarize and communicate information. They are of great importance, especially when there are numerical data involved, because when they are properly ordered, their interpretation is facilitated.

The quantities that are handled are called *variables*, which represent attributes of the magnitudes studied. They can be numerical, such as a measurement or age, or also qualitative, such as gender, hair color, or other.

Through tables and graphs, patterns are revealed that allow determining the relationship between the various variables. Without proper organization, these patterns could be hard to find, especially when the volume of data is large.

For its part, a graph is a drawing that allows the reader to appreciate existing patterns at a glance.

Tables are not only used to order numeric data, as will be seen shortly. They also serve to summarize relevant information about a topic, such as lists with formulas, characteristics, applications and examples, therefore, they constitute a wonderful study tool.

**Tables or charts**

They consist of an arrangement of grids, with rows and columns, duly identified. Information is placed on the grids, either numerical, text, or a combination of both.

A table must have a title that identifies it, as well as the different magnitudes and characteristics it contains. If they are numerical magnitudes, the unit of measurement used must be indicated, for example, a length must be specified in meters, kilometers, feet, miles or another suitable unit.

There are many types of tables, in what follows there are some examples that illustrate their use:

**1. Descriptive table or table**

It is used to summarize information about a topic and facilitate its study. Its design is very varied, including colors, different types of letters, icons and more, according to the convenience of the box designer.

Many word processors include layout options for creating tables and inserting them into the report or document. It should be noted that the chart or table does not necessarily contain all the information about the subject under study, but rather that which the author deems appropriate. The details can be expanded later in the body of the report.

As an example, a table is shown with the most notable physical characteristics of Titan, a natural satellite of the planet Saturn. Some researchers argue that this satellite meets the conditions to be colonized by humans in the future.

**2. Comparative table or table**

It is a resource used to compare concepts, ideas or magnitudes. You can include texts with descriptions and also numerical data. The following is a comparative table between the *imperatives* philosophical ideas of the thinker Immanuel Kant (1724-1804).

**3. Frequency table**

In descriptive statistics, it is convenient to group the data into frequencies, a resource that is useful for both quantitative and qualitative data.

The following table shows the speeds taken by radar, of 50 cars that passed through an avenue. The 50 data were organized into 6 classes, whose respective frequencies and class marks are shown. This table is used to later calculate the mean, variance, and standard deviation of the data.

**4. Table of values of a function**

The concept of mathematical function is key to modeling both natural phenomena and the most diverse situations. a variable function *x* It can be represented by a table of values.

Below is a table of values for the function f(x) = x2-4:

**5. Truth Table **

Truth tables are used in propositional logic to find out the truth value of propositions.

Next appears the truth table for the logical conjunction, which consists of a combination of two simple logical propositions through the letter «and», denoted by an inverted «v».

The conjunction is true (V) when statements p and q are true, as in «*The Moon and Titan are natural satellites*”, otherwise it is false (F). The truth values of the combinations are shown in the table:

**graphics**

Graphs are visual resources that facilitate data analysis by establishing the relationship between variables. They are widely used in areas such as basic sciences, statistics, economics, and social sciences.

The type of graph depends on the nature of the data being represented. Here are some examples of frequently appearing graphs:

**1. Graphs of functions**

For a function of one variable, graphing the function consists of plotting the ordered pairs (x, y) on the Cartesian plane. This consists of two lines perpendicular to each other, one of them horizontal, usually called the x-axis, and the other vertical, called the y-axis.

For the function f(x) = x2-4, whose table of values appears in the preceding section, its graph is easily drawn with spreadsheet-type software, or with an online graphing program.

**2. Bar graphs**

They allow to relate quantitative and qualitative variables, through horizontal or vertical bars.

The typical population pyramid is a good example of a bar graph. In it there is an annual breakdown of the population, by sex and age range.

**3. Pie charts**

They consist of a circle, which represents 100% of a given variable. The sizes of the circular sectors are proportional to the frequency with which a certain characteristic or attribute appears. The following example shows the graph by sectors of the English-speaking population in the world.

The area of each circular sector is proportional to the number of English speakers in a country, and is calculated by multiplying the number pi, the radius of the circle squared, and the width of the sector measured in degrees, and then dividing all by 360º.

**4. Organization chart**

It is a graphical representation of a hierarchical structure, such as that of a company or organization. In this way, the reader of a report appreciates at a glance the distribution of the main functions in said organization.

**5. Graphs of Fractions**

They are used to display a fractional number. In the image below to the left, the circle is divided into four equal parts, so the fraction ¼ represents one of those parts.

In the left image, the circle is divided into eight equal parts, one of them represents the fraction 1/8 and two of them are 2/8, which is equivalent to ¼.