Is there a better way to do this than using tabular?

Use \substack and \mathclap to pretend the large subscript has no width.

\documentclass{article}
\usepackage{mathtools}

\begin{document}

\[
\underbrace{2\quad 9\quad 10\quad 12}_{\text{$4$ elements}}
\quad
\underbrace{19\quad 22}_{
  \substack{
    \big\uparrow\\[3pt]
    \mathclap{\text{Median}=\frac{19+22}{2}=20.5}
  }
}
\quad
\underbrace{37\quad 39\quad 46\quad 50}_{\text{$4$ elements}}
\]

\end{document}

Note that \operatorname is no substitute for \mathrm or \text.

Maybe just placing an array below the underbrace.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Compute the median according to the above algorithm
\[
\underbrace{2\quad 9\quad 10\quad 12}_{4\text{ elements}}
\underbrace{19\quad 22}_{\begin{array}{c}
    \Big\uparrow \\[6pt] \operatorname{Median} = \frac{19+22}{2} = 20.5
\end{array}}
\underbrace{37\quad 39\quad 46\quad 50}_{4\text{ elements}}
\]
\end{document}