Browsing by Subject "mean"

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    Guess the Mean: Which Method is Better?
    (Depauw, 2020-08) Rashid, Mamunur; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    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.
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    Visualizing the mean and the standard deviation using R/RStudio Shiny package
    (2020) Hufnagel, Rachel; Chen, Ziyi; Rashid, Mamunur; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    Many of us have experienced an unpleasant situation in which only the mean and the standard deviation of a data set are reported, but we are expected to know everything about the dataset as if those two values were all we needed to know. We would learn so much more if there were easy ways to create and share graphical representations and interpretations of the entire raw data. In this paper, we not only explain what the mean and the standard deviation tell us about a data set, but also describe how to include additional information on the data. We utilize the work of Sarkar and Rashid (2016) that introduced a geometric visualization of the sample mean based on the empirical cumulative distribution function of the raw data. They also extended the idea to visualize measures of spread such as the mean deviation, the root mean square deviation and the standard deviation. Our research involves creating interactive applications of these methods using R/RStudio Shiny, an open source package that provides an elegant and powerful web framework for building web applications. We hope, upon publication of these tools, users all over the world will use such interactive visualization methods for learning, teaching, and building more advanced tools.