Definition 1.3.6. Alternate Percentile Definition.
For \(0 \lt s \lt 1\) and for order statistics \(y_1, y_2, ..., y_n\) define the 100s-th percentile to be
\begin{equation*}
P^{s} = (1-r)y_m + ry_{m+1}
\end{equation*}
where m is the integer part of \((n-1)s + 1\text{,}\) namely
\begin{equation*}
m = \left\lfloor (n-1)s + 1 \right\rfloor
\end{equation*}
and
\begin{equation*}
r = (n-1)s + 1 - m,
\end{equation*}
the fractional part of \((n-1)s+1\text{.}\)
In Excel, this is PERCENTILE.INC or just PERCENTILE.