\begin{frame}
  \frametitle{Group By}
  
  \begin{goal}{}
    ``Group by'' \emph{partitions} the rows of
    a table into \emph{disjoint groups}:
    \begin{itemize}
      \item based on \emph{value equality for the \sql{group by} attributes}.
    \end{itemize}
    Aggregation functions applied for each group separately.
  \end{goal}
  \pause
  \medskip
  
  \begin{code}{\textwidth}{Average points for \underline{each} homework}
    \footnotesize
    \parbox{0.4\textwidth}{%
      \BUseVerbatim{query}
    }
    \hfill
    \parbox{0.5\textwidth}{%
      \footnotesize\centering\ttfamily
      \colorbox{rellight}{%
        \begin{tabular}{|r|r|}
          \hline
          \hd{number} & \hd{avg(points)} 
          \\
          \hline
          1 & 8 \\
          2 & 8.5  \\
          \hline
        \end{tabular}%
      }
    }
  \end{code}
  All tuples agreeing in their \sql{number} values for a group:
  \begin{tcenter}
  \footnotesize\ttfamily
  \colorbox{rellight}{%
    \begin{tabular}{|r|r|r|r|}
      \hline
      \hd{sid} & \hd{category} & \hd{number} & \hd{points}  
      \\
      \hline
      101 & homework & 1 & 10 \\
      102 & homework & 1 &  9 \\
      103 & homework & 1 &  5 \\
      \hline\hline
      101 & homework & 2 &  8 \\
      101 & homework & 2 &  9 \\
      \hline
    \end{tabular}%
  }
  \end{tcenter}
\end{frame}