## Median

In the median statistics, numerical values - e.g. from a chronological order - are rearranged in such a way that a data table is created in which $n\mathrm{+}1$Readings $x$ are sorted according to size (order statistics):

- $${x}_{1}\le {x}_{2}\le \dots \le {x}_{\frac{n}{2}}\le {x}_{\frac{n}{2}+1}\le \dots \le {x}_{n+1}$$

If the number of values is odd ($n$ is an even natural number), the value in the middle is regarded as a characteristic value and referred to as the median or central value:

- $$\tilde{x}={x}_{\frac{n}{2}+1}$$

If there is an even number of in the table $n$ Measured values:

- $${x}_{1}\le {x}_{2}\le \dots \le {x}_{\frac{n}{2}}\le {x}_{\frac{n}{2}+1}\le \dots \le {x}_{n}$$

the mean of the two neighboring mean values is calculated (pseudomedian):

- $$\tilde{x}=\frac{1}{2}({x}_{\frac{n}{2}}+{x}_{\frac{n}{2}+1})$$

The median $\tilde{x}$ is a better measure of the most frequent value than the mean. This applies in all cases, but especially in the case of crooked or multi-peaked distributions.