Median

In statistics, the median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. For a data set, it may be thought of as the "middle" value. 


Finding the median in sets of data with an odd and even number of values. image: wikipedia


For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it.

The median is a commonly used measure of the properties of a data set in statistics and probability theory. 

Geometric visualisation of the mode, median and mean of an arbitrary probability density function. image: wikipedia

The basic advantage of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed so much by extremely large or small values, and so it may give a better idea of a "typical" value. 

Income and assets of groups

For example, in understanding statistics like household income or assets which vary greatly, a mean may be skewed by a small number of extremely high or low values. Median income, for example, may be a better way to suggest what a "typical" income is.

Because of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.


source adapted from: Median. (2017, October 19). In Wikipedia, The Free Encyclopedia. Retrieved 01:57, November 2, 2017, from https://en.wikipedia.org/w/index.php?title=Median&oldid=806139198