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Median of Numbers

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.

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Median of Numbers -

Tag(s) : Statistics, Data Processing

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# Median of Numbers

## Median Calculator

### How to compute a median value?

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).

### When to use the median function?

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

### How to find back values from the median?

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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