Mean values in practice

Abstract

Mean values are among the most frequently used statistical indicators/methods. The textbooks also discuss them in a fairly similar way and structure. In this article, we undertake to briefly summarize what we mean by mean value, within which we mainly deal with averages. We will review what types there are, and what are the properties of mean values/averages based on the literature (mainly economic Hungarian higher education curricula and Statistical Review articles). On the other hand, we expand the discourse on averages with some novel aspects, mainly in connection with the types of averages, their practical use, and the generalizations and variations of the most commonly used arithmetic average.First, we briefly describe the situational mean values, the limitations and advantages of their use, and the problems that arise in practice. After that, we move on to the characterization of the averages (calculated mean values). We show that, in theory, averages can be generalized in several ways, but in practice, in addition to the arithmetic average, other averages are only used in special cases. Especially in the case of using the harmonic mean, the priority of the aspect of practical application over theoretical systematization appears, and we give several examples of this. We take a closer look at the properties of the most commonly used arithmetic mean. We have presented a rarely used, but useful from a practical point of view, the so-called perceived average, as well as its relation to the traditional arithmetic average. In the last part of the article, we use an example to illustrate the possibilities of calculating the mean values, the relationship between the mean values, and the problems that may arise.