Vertical alignment of graphic and tabular

Whether you want both objects aligned at the top or at the bottom, you can use two minipage environments and apply the \vspace{0pt} trick to obtain the desired vertical alignment (a quirk of TeX/LaTeX).

See also Understanding minipages - aligning at top for more details.

Set the optional argument to both minipage environments to

• t for top alignment,
• b for bottom alignment.

Note: I've used tikzpicture environment as placeholder for your graph, as you didn't provide the code for that.

\documentclass{article}

\usepackage[demo]{graphicx}
\usepackage{tikz}

\begin{document}

\begin{minipage}[t]{.5\textwidth}
\vspace{0pt}
\raggedleft
    \begin{tikzpicture}
        \filldraw[draw=red,fill=red!20] rectangle (3,3);
    \end{tikzpicture}
\vspace{0pt}
\end{minipage}
\begin{minipage}[t]{.5\textwidth}
\vspace{0pt}
\raggedright
    \begin{tabular}{ll}
            p: 78\%&\\\\
            $\mu$: -7\% & $\sigma$: 7\%\\
            $\alpha$: 0.43 & N: 11977
    \end{tabular}
\vspace{0pt}
\end{minipage}  

\end{document}

You can use the adjustbox package which does all the work without you setting any length. Just change the mock tikzpicture with your plot.

\documentclass{article}

\usepackage{tikz}
\usepackage{adjustbox}

\begin{document}

\section{Centered alignment}

\begin{adjustbox}{valign=c}
\begin{tikzpicture}
  \filldraw[draw=red,fill=red!20] rectangle (3,3);
\end{tikzpicture}
\end{adjustbox}
\begin{tabular}{ll}
  p: 78\%&\\[2ex]
  $\mu$: -7\% & $\sigma$: 7\%\\
  $\alpha$: 0.43 & N: 11977
\end{tabular}

\section{Top alignment}

\begin{adjustbox}{valign=t}
\begin{tikzpicture}
  \filldraw[draw=red,fill=red!20] rectangle (3,3);
\end{tikzpicture}
\end{adjustbox}
\begin{tabular}[t]{ll}
  p: 78\%&\\[2ex]
  $\mu$: -7\% & $\sigma$: 7\%\\
  $\alpha$: 0.43 & N: 11977
\end{tabular}

\section{Bottom alignment}

%\begin{adjustbox}{valign=b} % adjustbox not really needed
\begin{tikzpicture}
  \filldraw[draw=red,fill=red!20] rectangle (3,3);
\end{tikzpicture}
%\end{adjustbox}
\begin{tabular}[b]{ll}
  p: 78\%&\\[2ex]
  $\mu$: -7\% & $\sigma$: 7\%\\
  $\alpha$: 0.43 & N: 11977
\end{tabular}

\end{document}