While students generally have a good intuition for means prior to entering an introductory course in statistics or probability, the concept of a standard deviation is likely to be quite new. Formulas for the standard deviation in various situations are given which must either be accepted on faith or derived algebraically, depending on the mathematical strength of the student.
In this paper, we present an imprecise measure of variation, the graphical spread, which students can measure directly from plots of probability density functions, probability mass functions, or histograms of data. Without any algebraic work, students can develop an intuition for how reasonable measures of spread, such as the standard deviation, depend on the parameters of a specific probability distribution or on the sample size.
Department Technical Reports