Guess the Mean: Which Method is Better?

Abstract

The mean of a set of numbers may be guessed in one of two ways: (1) as a fulcrum placed under the dot plot; or (2) as a vertical line that equalizes areas of two regions bounded by the step plot (also known as the empirical cumulative distribution function). Which of these two methods is better? We design, conduct and analyze a statistical experiment to address this question. While our findings support better performance by the latter method at the aggregate level, each individual user may respond differently to the question. We hope all users will learn both methods and determine for themselves which method they are better at. We also hope educators will empower their students by including both methods in their syllabi.