On a Case of Inadequacy in Using the Arithmetic Mean

• Published in: Procedia economics and finance 2014, Vol.10, p.134-140
• Main Author: Dragan, Irina-Maria
• Format: Article
• Language: English
• Subjects: arithmetic mean (average); Cauchy distribution; heterogeneous populations; SMEs
• ISSN: 2212-5671; 2212-5671
• DOI: 10.1016/S2212-5671(14)00286-X

In strong heterogeneous populations, the use of the average indicator is not appropriate in order to summarize the values, because this involves a relatively homogeneous population and a normal, or approximately normal, distribution around the central value. In the case of some genuine economic processes, there is any possibility to apply even the homogenization process of data, by taking into consideration the string boundaries as outliers’ values, as it can be proceed with a series of measurements. In such heterogeneous populations, the characteristic respect a Cauchy distribution, which is somewhat similar to Gauss-Laplace distribution, however it has more elongated tails and a specific density of the distribution. For these cases it is appropriate as the middle value to be established through the median. The case study, conducted and released in this paper, refers to the financial performance of SMEs. This population is characterized by a strong heterogeneity, so in this case the merger at the level of the population is risky by using the mean, because it generates distorted indicators of the shaped reality. The obtained results in this research might represent a guide for the study of situations in which there are heterogeneous populations, moreover where it is not possible to clean their extreme values.