Mean and Median

… a core concept used in Quantitative Methods and Atlas104

Click for OnlineStatBook page

Concept description

OnlineStatBook (reference below) defines:

  • mean (or arithmetic mean) of a variable is given by (the sum of all its values)/(the number of values)
  • median is the 50th percentile of a distribution.

OnlineStatBook notes that the mean is “perhaps the most common measure of central tendency” and “typically what is meant by the word “average”.” However, “[d]espite its popularity, the mean may not be an appropriate measure of central tendency for skewed distributions, or in situations with outliers.” It notes that the median is also a popular measure of central tendency and that the median is often more appropriate than the mean in skewed distributions and in situations with outliers. OnlineStatBook notes when a distribution is symmetric, then the mean and the median are the same.

OnlineStatBook describes how that the mean is the point on which a distribution would balance [see image above], the median is the value that minimizes the sum of absolute deviations, and the mean is the value that minimizes the sum of the squared deviations.

Atlas topic, subject, and course

Describing Distributions (core topic) in Quantitative Methods and Atlas104 Quantitative Methods.

Sources

David M. Lane and Heidi Ziemer, OnlineStatBook, at http://onlinestatbook.com/2/summarizing_distributions/what_is_ct.html, accessed 10 June 2017.

OnlineStatBook, Glossary, at http://onlinestatbook.com/2/glossary/index.html, accessed 10 June 2017.

Page created by: Ian Clark, last modified 10 June 2017.

Image: OnlineStatBook, at http://onlinestatbook.com/2/summarizing_distributions/mean_median_defM.html, accessed 10 June 2017.