Abstract
This chapter introduces the concept of averaging aggregation. Usually when an ‘average’ or ‘mean’ is required, we will calculate the arithmetic mean, which is the sum of all numbers divided by how many there are. However, the arithmetic mean is just one example among many functions that can be classed as ‘averaging’. Averaging functions are used to summarize sets of numbers in a way that gives a representative idea of what is normal. We will see that in some situations, it is neither useful nor appropriate to use the arithmetic mean. We provide examples of other useful averaging functions including the median, the geometric mean and the harmonic mean and give an overview of their properties. The chapter includes worked examples and questions, as well as an introduction to the R programming language and how these functions can be implemented.
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Notes
- 1.
This broader definition of a function extends to computer functions and algorithms too. An object, file, image, etc., is submitted and an output is produced.
- 2.
Generated using the f.plot3d() function from the AggWAfit library available from http://www.researchgate.net/publication/306099814_AggWAfit_R_library or alternatively http://aggregationfunctions.wordpress.com/book.
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James, S. (2016). Aggregating Data with Averaging Functions. In: An Introduction to Data Analysis using Aggregation Functions in R. Springer, Cham. https://doi.org/10.1007/978-3-319-46762-7_1
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