Tool for calculating the median from a list of values. The median of a list of numbers is a statistical value illustrating in part the distribution of numbers in the list.

Median of Numbers - dCode

Tag(s) : Statistics, Data processing

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Tool for calculating the median from a list of values. The median of a list of numbers is a statistical value illustrating in part the distribution of numbers in the list.

Take a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n \} $ ranked in ascending order. To calculate the **median** of this set of values, take the value in the middle of this list (with as much value on the left as on the right).

Thus, if the list has an odd number ($ 2N+1 $) of elements, the **median** is the value of the (N+1)-th element. If the list has an even number ($ 2N $) of elements, the **median** is the average value (arithmetic mean) between element N and element N+1.

__Example:__ The list of 8 elements: 13,5,1,3,21,1,2,8 is sorted by ascending order 1,1,2,3,5,8,13,21. Its **median** is 4, the mean between the digits 3 and 5 (respectively in 4th and 5th position in the list, like this, there are 4 smaller values and 4 larger values).

__Example:__ The list of 5 elements: 1,100,1000,10000,10 is sorted 1,10,100,1000,10000. Its **median** is the value at the center of the list: 100 (in position 3, like this, there are 2 smaller values and 2 larger values).

The **median** is generally used in statistics to represent a central tendancy for value sets with a long tail. Indeed the series of numbers whose most of the elements is outside the normal distribution are poorly represented by the average/mean value, the **median** is generally preferred in these cases.

__Example:__ The **median** is used for salaries to get the **median** income

It is impossible to find back the original values from a **median** value. There is an infinity of set of values having the same **median**.

__Example:__ 1,3,5 has the same **median** as -1,0,3,1000,1000000000

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