# What is a frequency table : a general introduction in the modern statistical apparatus

In truth, modern statistics is widely used in all spheres of scientific researches. However, it would be unfair to suggest that this mathematical method of collection, analysis, visualization, classification and ordering data is used only in highly specialized researches. Furthermore, modern statistics finds its application in virtually all spheres of science and management. Modern economics, medicine, history astronomy, management, biology, sociology, architecture, anthropology, physics, – all these scientific disciplines would be virtually useless without the use of separate methods of classification and analysis of data. Moreover, statistics finds its reflection even in various spheres of mundane life, such as fashion, cooking, tourism, gardening, sport, etc. Obviously, a complete and profound ownership of basic statistical methods is absolutely necessary for all students and applicants, regardless of their chosen disciplines or courses of study. After all, how can a student suppose that she knows how to write a coursework if she does not understand the fundamental principles of modern statistics?

Therefore what is the statistics? We can trace the history of the word ‘statistics’ up to the times of great Roman Empire, in which the principal rules of statistics and mathematics were invented and successfully evolved. The Latin word ‘status’ means ‘the condition of something or someone and/or the current situation’. Statistics deals with the study of the quantitative aspects of virtually all physical phenomena and processes in different numeral forms. It also allows us determine, identify, isolate and examine inner patterns and interconnections between different phenomena from various fields of study that may not seem related to each other at first sight. In other words, the primal subjects of mathematical statistics are developing methods of producing scientifically based conclusions about random events on the results of an experiment, observations, computations, etc. In order to visualize obtained data, we can select various methods of data presentation. Doubtlessly, one of the most demonstrative and, simultaneously, simple methods of representation is to compose a standard frequency table. Thereby, let us move on to the next question: what is a frequency table ?

A frequency table is one of the most widely used methods of summarizing data. A frequency table represents and circumscribes the number of times a data value intervenes. The simplest sample of a frequency table can be represented in a form of a table with three separate columns. The first column contains data about intervals. The range in data values determines the necessary amount of intervals. Please note that all intervals should be of equal size. In addition, one has to verify the measures of all intervals in order to prevent overlaps between them. All intervals should be built in strict accordance with the range in data values. One has to remember that the smaller the deviation is, the better the accuracy is. The second column represents the calculated results and the last column includes the tally marks. Therefore, a frequency table allows us to determine the frequency results. Do not forget that you should enter the data into the frequency table very scrupulously and attentively, avoiding inaccuracies and errors from the very beginning. In general, this process is quite similar in principle to writing a synthesis essay. You have to collect all previously received results and computations, verify their value, categorize them according to their magnitude and place them in the correct order. As a result, you will get a differentiated register, which demonstrates various interrelations between the different groups of specific units. Frequency and relative frequency tables are excellent methods of visualizing information and they are especially useful for analysis of data, which is categorized into several groups.

## What is a frequency table : different variants and modifications of frequency tables

A group frequency table (as opposed to a simple table) comprises a list of groups or series of units in accordance with some specific feature, which is typical for all units. The simplest form of a group table is a table, which represents the distribution of specific ranks. Obviously, the most commonly used modification of the frequency tables is the simple table, because it allows us to analyze our results, eschewing unnecessary recalculations and oversophisticated manipulations with specific indexes.

### How to formalize a standard frequency table or what is a frequency table from a standpoint of modern statistics

Naturally, each modification of the frequency tables has to be presented in a standard official format with an eye to ease calculations and representation of the obtained results. Here is a concise register of basic rules that may be useful for constructing standard frequency tables:

• A frequency table should be compact. It should contain only the raw data that directly reflect the studied phenomenon in statics and/or dynamics
• The table header, the names count and lines should be clear, concise and laconic. The title should reflect all significant information about the object, such as the sign, date and location of each specific event. In other words, every specific exemplum of frequency tables must be accompanied by a particularized variation of a standard cover letter, which contains all necessary information about the previously performed computations, goals of the research, intermediate stages of the research, etc.
• All columns and rows should be numbered and categorized. Unfortunately, those students who complete their computations in a hurry often ignore it. Remember, that even the slightest error can deface all your further computations, thereby, you should verify all your records with an eye to eschew considerable distortions of data.
• All columns and rows must contain the units for which there exist a set of standard abbreviations.
• Units should be grouped into different columns. This little step significantly facilitates the further process of comparison and computation.
• For ease of reading and further calculations all numbers in the statistical table should be represented in the middle of the graphs. For example, we should represent each unit under the other connected units.
• In addition, it is also advisable to round numbers to the same degree of accuracy.
• You should use the designation 0.0 or 0.00 in order to display small numbers.
• If the number is obtained on the basis of imputation, it has to be taken in brackets. The number of questionable results has to be accompanied by a question mark.

#### How to analyze a frequency table: modern methods of analysis

The previous paragraphs show us what is a frequency table. Of course, even the most complete and informative frequency table provides us only a concise list of results and a register of concrete groups, which are isolated according to the specific feature. In other words, a frequency table is used as a special custom paper for further computations. Therefore, let us study the main principles of analysis in order to make a response to the question: ‘what is a frequency table ?’ more informative and descriptive. There exist two main methods of analysis: structural and meaningful. A content analysis permits us to examine the inner patterns of our table and determines the different considerable characteristic of our research, such as interconnections between various individual groups, which are relevant to each other, relationships of specific groups of units and/or concatenations between separated events or issues. A structural analysis studies diverse signs of the relation of subject and predicate indicators, and specific quantitative and attributing signs. Analysis of different modifications of frequency tables allows us to characterize various types of specific phenomena, the structure of population, ratios and proportions between groups and units of observation; identifying the nature and direction of the relationships and interdependencies between the various isolated groups or clusters. Analysis of individual units and clusters must start with an examination of the absolute values. Only after this stage of calculations, we can analyze their relative values. In addition, we should consider the dynamics of each characteristic for the entire period while passing from one to another. The previously mentioned methods of analysis can be supplemented by the computation of relative and average values if required by the research. In order to receive a more complete and intuitive understanding of the studied phenomena and processes, according to the particularized modification of frequency tables, we can construct different graphs, charts, linear diagrams, etc.

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