This article presents a new method for introductory teaching of the sample mean, median and mode(s) from a univariate dataset. These basic statistical concepts are taught at various levels of education from elementary school curriculums to courses at the tertiary level. These descriptive measures of location can be taught as optimized solutions to certain loss functions. Although proving these require some understanding of derivatives as used in a first year calculus course, the attained insight is valuable for higher level statistical thinking. Using the statistical computing software R, we visually illustrate the minimization of these loss functions using some example datasets.