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. The median of this set of values is the value in the middle of this list.

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 in ascending order 1,1,2,3,5,8,13,21. Its median is 4, the mean between the values 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 to represent 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

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