Similarly, the 75th percentile is given by
\begin{equation*}
(n+1)s = (4+1)0.75 = 15/4 = 3.75\text{.}
\end{equation*}
So, m = 3 and r = 0.75. Therefore
\begin{equation*}
P^{0.75} = 0.25 \times 8 + 0.75 \times 10 = 9.5
\end{equation*}
It is interesting to note that 3 also lies between 2 and 5 as does 2.75 and has the same percentages above (75 percent) and below (25 percent). However, it should designate a slightly larger percentile location. Indeed, going backward:
\begin{gather*}
3 = (1-r) \times 2 + r \times 5\\
\Rightarrow r = \frac{1}{3}\\
\Rightarrow (n+1)s = 1 + \frac{1}{3} = \frac{4}{3}\\
\Rightarrow s = \frac{4}{15} \approx 0.267
\end{gather*}
and so 3 would actually be at approximately the 26.7th percentile.