Naturally, it is an unacceptable logical blunder to consider that different types of statistical averages, such as mean, median, mode and/or range, are not widely used in various spheres of study, which are not based on math and statistics. On the contrary, profound understanding of the main characteristics of these types of averages and methods of their calculation are necessary for any educated person. For example, it can be effective to represent the entire data series by using a single value, which characterizes the ‘average’ value of the entire series when analyzing diverse large data sets. In other words, in order to simplify cumbersome computations, indicate the main properties of the data set and/or determine the main elements of the data set we can determine the so-called central tendency. Therefore, mean, median, mode and range can be defined as the most demonstrative ways to describe it. Obviously, these characteristics are widely used in those fields of study, which require a great number of different operations with large data sets because their statistical value is in direct proportion to the quantity of objects represented in the given set. For example, such statistical ‘averages’ as mean, median, mode allow us to determine the characteristic properties of the series with sufficient precision, whereas the range is representative only in case of large data sets. Let us explain it using a simple example. According to the definition of the range, if the data set is small and the difference between the smallest and the largest values in the series is small than the central tendency of this series (mean, median, mode, etc.) is not representative. Therefore, all these properties of fundamental statistical ‘averages’ make them indispensable for virtually all statistical calculations. For example, statistics as well as IT specialists need to perfectly understand the characteristics of mean, median, mode and range in order perform various statistical measurements, manage systems, plan capacity and balance load, monitor maintenance and troubleshoot issues, etc. Obviously, these different objectives dictate that these specialists calculate mean, median, mode, range and/or diverse types of their combinations, attempting to demonstrate a statistically significant quantity, trend or deviation from the norm of the data set. Of course, determining mean, median, mode and range is only the start, however, they permit us to determine the central tendency of the data set from the very beginning.
As it was already emphasized, mean, median, mode and range appertain to the group of fundamental mathematical terms, which are used in practically all branches of modern statistics, accounting, financial management, budget planning, various areas of computer science, etc. Obviously, with an eye to achieving a satisfying understanding of these doubtlessly significant mathematical terms, it is recommended to examine not only their main mathematical properties and methods in which they may be used in practically oriented assignments but also different techniques used to find them. This educational operation has several aims. Firstly, by studying the simplest methods according to which these ‘averages’ can be determined, one will inevitably achieve a better understanding of basics of statistics. In fact, this topic may serve as a rich source of different mathematical exercises and practical assignments, thereby, by performing these simple computations one can considerably improve her logical skills. Secondly, this topic supply students with a great amount of objectives, which require not only an ability to create abstract mathematical models but also the ability to relate theoretical information with practical problems. Therefore, its importance for those students who study economics, computer science, accounting, management or architecture can hardly be overestimated. Thirdly, by comparing these ‘averages’ between each other and studying differences between them, one can understand not only a mathematical but also a practical meaning of these conceptions, which is, obviously, important for future specialists. Thus, in order to achieve all these goals let is examine the definitions of mean, median, mode and range, as well as their significant differences. Here is a concise list, which includes also characteristic examples and elementary exercises targeted at simplifying of the educational material: