Visualizing Mean, Median, Mean Deviation, and Standard Deviation of a Set of Numbers. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Sarkar, Jyotirmoy; Rashid, Mamunur
• Is Part Of: American statistician. Volume 70:Issue 3(2016)
• Page Start: 304
• Page End: 312
• Publication Date: 2016-07-02
• Subjects: Center -- Empirical cumulative distribution function -- Fulcrum -- Mean squared deviation -- Minimization -- Prism -- Solid of revolution -- Spread -- Variance; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2016.1165734
• Languages: English
• ISSNs: 0003-1305

Abstract

ABSTRACT: We review the existing visualizations of the mean and the median of a given set of numbers. Then we give an alternative visualization of the mean using the empirical cumulative distribution function of the given numbers. Next, we visualize the mean deviation (MD) and the mean square deviation (MSD) of the given numbers from any arbitrary value, including the variance. In light of these new visualizations, we revisit the well-known optimal properties of the MD from the median and the MSD from the mean. We also give a more elementary explanation of why the denominator of the sample variance of a set of numbers is one less than the sample size.