# 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.