Editing Box plot (section)

==== General equation to compute empirical quantiles ====

: <math>q_n(p) = x_{(k)} + \alpha(x_{(k+1)} - x_{(k)})</math>

: <math>\text{with } k = [p(n+1)] \text{ and } \alpha = p(n+1) - k</math>
:Here <math>x_{(k)}</math> stands for the general ordering of the data points (i.e. if <math>i<k</math>, then  <math>x_{(i)} < x_{(k)}</math> )

Using the above example that has 24 data points (''n'' = 24), one can calculate the median, first and third quartile either mathematically or visually.

'''Median'''
: <math>
\begin{align}
q_n(0.5) & = x_{(12)} + (0.5\cdot25-12)\cdot(x_{(13)}-x_{(12)}) \\[5pt]
& = 70+(0.5\cdot25-12)\cdot(70-70) = 70^\circ\text{F}
\end{align}
</math>

'''First quartile'''
: <math>
\begin{align}
q_n(0.25) & = x_{(6)} + (0.25\cdot25-6)\cdot(x_{(7)}-x_{(6)}) \\[5pt]
& = 66 +(0.25\cdot25 - 6)\cdot(66-66) = 66^\circ\text{F}
\end{align}
</math>

'''Third quartile'''
: <math>
\begin{align}
q_n(0.75) & = x_{(18)} + (0.75\cdot25-18)\cdot(x_{(19)}-x_{(18)}) \\[5pt]
& =75 + (0.75\cdot25-18)\cdot(75-75) = 75^\circ\text{F}
\end{align}
</math>