Handling of Univariate Data

  • Surendra P. VermaEmail author


It is not a common practice in element geochemistry to obtain truly univariate data having both central tendency and dispersion parameters, although, traditionally, this branch of geosciences (geochemistry) is based on such statistical information. The common but erroneous practice in geochemistry of measuring an “unknown” sample only once is pointed out. The major and trace element data of geochemical reference materials (GRMs) would approximately fit into the category of univariate data. The Gaussian distribution for the statistical population and the Student t distribution for the finite-sized samples are then presented. The visual technique of histograms is briefly pointed out. The inter-laboratory data for the GRM BHVO1 compiled from numerous literature sources are used to illustrate the statistical procedures for handling of univariate data. The presence of discordant outliers is one of the most ubiquitous problems in the GRM data. The relevant statistical parameters, robust as well as outlier-based, are presented and discussed in detail. However, it is stressed that the outlier-based methods should only be applied to normally distributed discordant outlier-free data arrays. Uncertainty or error propagation is then discussed, along with an example of density measurements. The approximate nature of these equations is documented and an alternative Monte Carlo approach is suggested. The chapter concludes with the four well known moments of a distribution and two newly proposed moments, which are mentioned for the first time in any book.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Instituto de Energías RenovablesUniversidad Nacional Autónoma de MéxicoTemixcoMexico

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