added 2 definitions

Author: JoramSoch

D/med.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-15 10:53:00
+
+title: "Median"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Measures of central tendency"
+definition: "Median"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Median"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-15"
+    url: "https://en.wikipedia.org/wiki/Median"
+
+def_id: "D101"
+shortcut: "med"
+username: "JoramSoch"
+---
+
+
+**Definition:** The median of a sample or random variable is the value separating the higher half from the lower half of its values.
+
+<br>
+1) Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a [sample](/D/samp) from a [random variable](/D/rvar) $X$. Then, the median of $x$ is
+
+$$ \label{eq:med-samp}
+\mathrm{median}(x) = \left\{
+\begin{array}{cl}
+x_{(n+1)/2} \; , & \text{if} \; n \; \text{is odd} \\
+\frac{1}{2}(x_{n/2} + x_{n/2+1}) \; , & \text{if} \; n \; \text{is even} \; ,
+\end{array}
+\right.
+$$
+
+i.e. the median is the "middle" number when all numbers are sorted from smallest to largest.
+
+<br>
+2) Let $X$ be a continuous [random variable](/D/rvar) with [cumulative distribution function](/D/cdf) $F_X(x)$. Then, the median of $X$ is
+
+$$ \label{eq:med-rvar}
+\mathrm{median}(X) = x, \quad \mathrm{s.t.} \quad F_X(x) = \frac{1}{2} \; ,
+$$
+
+i.e. the median is the value at which the CDF is $1/2$.

D/mode.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-15 11:10:00
+
+title: "Mode"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Measures of central tendency"
+definition: "Mode"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Mode (statistics)"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-15"
+    url: "https://en.wikipedia.org/wiki/Mode_(statistics)"
+
+def_id: "D102"
+shortcut: "mode"
+username: "JoramSoch"
+---
+
+
+**Definition:** The mode of a sample or random variable is the value which occurs most often or with largest probability among all its values.
+
+<br>
+1) Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a [sample](/D/samp) from a [random variable](/D/rvar) $X$. Then, the mode of $x$ is the value which occurs most often in the list $x_1, \ldots, x_n$.
+
+<br>
+2) Let $X$ be a [random variable](/D/rvar) with [probability mass function](/D/pmf) or [probability density function](/D/pdf) $f_X(x)$. Then, the mode of $X$ is the the value which maximizes the PMF or PDF:
+
+$$ \label{eq:mode-rvar}
+\mathrm{mode}(X) = \operatorname*{arg\,max}_x f_X(x) \; .
+$$