<P> With an even number of observations (as shown above) no value need be exactly at the value of the median . Nonetheless, the value of the median is uniquely determined with the usual definition . A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid . </P> <P> In a population, at most half have values strictly less than the median and at most half have values strictly greater than it . If each group contains less than half the population, then some of the population is exactly equal to the median . For example, if a <b <c, then the median of the list (a, b, c) is b, and, if a <b <c <d, then the median of the list (a, b, c, d) is the mean of b and c; i.e., it is (b + c) / 2 . Indeed, as it is based on the middle data in a group, it is not necessary to even know the value of extreme results in order to calculate a median . For example, in a psychology test investigating the time needed to solve a problem, if a small number of people failed to solve the problem at all in the given time a median can still be calculated . </P> <P> The median can be used as a measure of location when a distribution is skewed, when end - values are not known, or when one requires reduced importance to be attached to outliers, e.g., because they may be measurement errors . </P> <P> A median is only defined on ordered one - dimensional data, and is independent of any distance metric . A geometric median, on the other hand, is defined in any number of dimensions . </P>

When was the concept of expected value first devised and why