Hey, I asked my teacher for a standard equation for the median of a sample, she said there was no specific one.

I called lies, but I could not find it online.

Thus, the only choice was to ponder it for a long time.

(and I will define the terms, I tried to make it formal but I suck at that part of maths so far I think.)

$\displaystyle M_{ed}=\left\{\begin{matrix}

\left [\left (i_{\frac{1}{2}\left | x \right |+1}\right )+i_{\left | x \right |\frac{1}{2}\right ]}\frac{1}{2}; \mathbf{if}\left \{ \left | x \right |\in t|t=2n \right \}\\

i_{\frac{1}{2}\left | x \right |+\frac{1}{2}};\mathbf{if}\left \{ \left | x \right |\in j|j=2n+1 \right \}

\end{matrix}\right.$

Always puting the set in order from least to greatest first of course.

Terms defined:

Edit: The letter I is a representation of an element of x

If we have a population (P) then:

$\displaystyle x \subseteq P$

and $\displaystyle \left | x \right | $ is the number of element the set of data contains.

Is this correct? If I am not clear on something or made a notation mistake just tell meh.

Examples:

$\displaystyle c=\left \{ 1,2,3,4,5,6 \right \}\Rightarrow \left | c \right |=6\Rightarrow c\in 2n \therefore M_{ed}=\frac{c_{4}+c_{3}}{2}=\frac{4+3}{2}=3.5$

$\displaystyle t=\left \{1,2,4,8,10,4}\right \} \Rightarrow t=\left \{1,2,4,4,8,10 \right \}$

$\displaystyle |t|=6\therefore M_{ed}=\frac{t_3+t_4}{2}=\frac{4+4}{2}=4$