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This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In this paper, we show that Paul Samuelson (1915-2009), renowned as one of the main advocates of the mathematization of economics, has also contributed to the change of the place of visual representation in the discipline. In his early works (e.g. Foundations of Economic Analysis published in 1947), he rejected diagrammatic analysis as a relevant tool of theorizing but used diagrams extensively, both as a pedagogic tool in his introductory textbook Economics (1948) and as a way of clarifying his theory of public expenditure (1954-5). We show that Samuelson's reluctance to use diagrams in his early works can be explained by his training at Chicago and Harvard and his rejecting Marshall's economics, whereas his adoption of visual language in Economics was a product of the peculiar context affecting American mass-education after WWII. A methodological debate which opposed him to Kenneth Boulding in 1948 led him to reconsider the place of visual representation in order to clarify conceptual controversies during subsequent debates on mathematical economics. Therefore, it can be said that the prominent place of visual language in the diffusion of economic ideas was stabilized in the mid- 1950s, as mathematical language became the prevailing tool of economic theorizing. From this, we conclude that the idea that algebra simply upstaged geometry in the making of economic analysis must be qualified. [ABSTRACT FROM AUTHOR]