Have a look at Median Definition

If we arrange a finite list of numbers in ascending or descending order, the value that comes in the middle is the median in math (e.g., the median of [7, 9, 11, 13, 15] is 11). You think, this is it?? No, Median math is not so simple, If the number of data is an even number, then there is no single middle value; the median is then generally defined by the mean of the two middle values.

e.g. for (2, 4, 6, 8, 11, 15)

median is (6 + 8) / 2

= 14 / 2

= 7

If data is repeated in our list we will write it together in ascending or descending order.

e.g. for (9, 10, 17, 17, 20, 20, 22, 23)

median is (17+21) / 2

= 37 / 2

= 18.5

A median is only defined on ordered one-dimensional data, and is free of any distance metric. A geometric median is defined in any number of dimensions.

Now let us check what are the benefits offered by median that prompted mathematician to define median in math. The median can be more useful than the mean in case like, there are extreme values in the data set as it is not affected by the extreme values. The median is the most commonly used quoted quantity to measure property prices. The use of the median prevents from the problem of the mean property price which is influenced by a few expensive properties that are not representative of the general property market. Thus you have understood what is median in math, how it can be found and where it can be used.

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