Editing Percentile (section)

====First variant, ''C'' = 1/2====
[[File:Percentile interpolation.png|thumb|450px|The result of using each of the three variants on the ordered list {15, 20, 35, 40, 50}]]
(Sources: Matlab "prctile" function,<ref>{{cite web
|url=http://www.mathworks.com/access/helpdesk/help/toolbox/stats/prctile.html   
|title=Matlab Statistics Toolbox – Percentiles
|access-date=2006-09-15}}, This is equivalent to Method 5 discussed [[Quantile#Estimating the quantiles of a population|here]]</ref><ref>{{cite journal|last1=Langford|first1=E.|title=Quartiles in Elementary Statistics|journal=Journal of Statistics Education|date=2006|volume=14|issue=3|doi=10.1080/10691898.2006.11910589|doi-access=free}}</ref>)
: <math>x=f(p)=\begin{cases}
Np+\frac{1}{2},\forall p\in\left [p_1,p_N\right ], \\
1,\forall p\in\left [0,p_1\right ], \\
N,\forall p\in\left [p_N,1\right ].
\end{cases}</math>
where
: <math>p_i=\frac{1}{N}\left(i-\frac{1}{2}\right),i\in[1,N]\cap\mathbb{N}</math>
: <math>\therefore p_1=\frac{1}{2N}, p_N=\frac{2N-1}{2N}.</math>
Furthermore, let
: <math>P_i=100p_i.</math>
The inverse relationship is restricted to a narrower region:
: <math>p=\frac{1}{N}\left(x-\frac{1}{2}\right),x\in(1,N)\cap\mathbb{R}.</math>