$x$ is a variable which take its real values in the interval $[\min x, \max x]$ and $c$ is a real constant value that I want to determine. I want to determine a fixed value for $c$ such that $x/c$ approaches $1/2$ for any value of $x$ in $[\min x,\max x]$.
That is, I want that for any value of $x$ (in the interval $[\min x, \max x]$), $x/c$ approximates $1/2$. How can I determine a reasonable value of $c$ for this purpose (i.e. the most convenient value of $c$ such that $x/c$ is usually near $1/2$)?
Maybe by resolving an equations which looks like
$\int_{\min x}^{\max x} \frac{x}{c} dx = \frac{1}{2},$
or something similar? Or by making use of the average value of all possible values of $x$?
This is an example with a finite set of values that $x$ can take (not an interval):
Suppose that $x$ take its values from the set $X = \{2, 5, 6\}$, thus maybe a good value to choose for $c$ is $c = (2+5+6)\cdot2/3 = 26/3$, because the values $2/c$ and $5/c$ and $6/c$ are all not very far from $1/2$. This is the same as saying that $(2/c+5/c+6/c)/|X| = 1/2$ which gives $c = 26/3$. Thought, I don't know if there a more optimal value than $(2+5+6)\cdot2/3$ for this example ...
EDIT1: clarification of what I want to do:
Suppose I have a jar $E$ containing $6$ elements $\{e_1,e_2,e_3,e_4,e_5,e_6\}$ mapped to a set $X$ of $6$ values: $X = \{x_1=2, x_2=4, x_3=6, x_4=1, x_5=8, x_6=3\}$. I take each element $e_i$ from $E$ and put it in another jar $E'$ with a probability of $x_i/c$ (if the probability event of $x_i/c$ occurs, I put $e_i$ in $E'$). At the end, I want that the number of elements in the jar $E'$ equals approximately the half of the number of elements of $E$, that is, for this example ideally the number of elements in $E'$ will be $6/2=3$. How to determine a fixed value of $c$ in order to do that? I guess that the problems turns out to finding the value of $c$, such that for any value $x_i$, the probability $x_i/c$ approximates $1/2$, right?
Ok the answer is probably to choose $c$ as $2$ times the average value of $x_i$.
EDIT2: the second problem (more difficult) after joriki's answer:
Suppose this time that each value $x_i$ is actually the $\min$ distance between the corresponding item $e_i$ and the items that are already in $E'$. That is with previous example:
We have $E = \{e_1,e_2,e_3,e_4,e_5,e_6\}, X = \{\max x, ?, ?, ?, ?, ? \}$
We put $e_1$ in $E'$ according to probability $x_1/c$ which is $1$, thus: $E = \{e_2,e_3,e_4,e_5,e_6\}, E' = \{e_1\}$, and $X = \{x_1=\max x, x_2=\min_{e_j \in {E'}}(e_2,e_j), ?, ?, ?, ?\}$
We put $e_2$ in $E'$ according to probability $x_2/c$, thus: $E = \{e_3,e_4,e_5,e_6\}, E' = \{e_1,e_2\}$, and $X = \{\max x, x_2, x_3=\min_{e_j \in {E'}}(e_3,e_j), ?, ?, ?\}$
And so on ...
So how to determine $c$ in this case ?