## Median |

in

andstatistics , theprobability theory **median**is the value separating the higher half from the lower half of a , adata sample or apopulation . for aprobability distribution , it may be thought of as the "middle" value. 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 adata set , the median is the value such that a number is equally likely to fall above or below it.continuous probability distribution the basic advantage of the median in describing data compared to the

(often simply described as the "average") is that it is notmean so much by a small proportion of extremely large or small values, and so it may give a better idea of a "typical" value. for example, in understanding statistics like household income or assets, which vary greatly, the mean may be skewed by a small number of extremely high or low values.skewed , for example, may be a better way to suggest what a "typical" income is. because of this, the median is of central importance inmedian income , as it is the mostrobust statistics , having aresistant statistic of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.breakdown point - finite data set of numbers
- probability distributions
- populations
- jensen's inequality for medians
- medians for samples
- multivariate median
- median-unbiased estimators
- history
- see also
- references
- external links

In **median** is the value separating the higher half from the lower half of a

The basic advantage of the median in describing data compared to the