\begin{table}%t4
\caption{\label{Tab:frequency}Summary of the binary frequency among different samples of~K and M~giants.}
%\centerline
 {\small \begin{tabular}{lllll}
\hline \hline
Stellar type & Sample properties & $N_{\rm tot}$ & Binary frequency (\%) & Ref.\\
\hline 
Field MIII & I (whatever $N\ge 2$, all $Sb$) & 771 & 5.6 & Sect.~\ref{Sect:freqI}\\
           & II, III, IV ($N > 4$, all $Sb$) & 254 & 9.8 (+2.4?) & Sect.~\ref{Sect:freqII}\\
Field MIII (without Miras)  & I (whatever $N\ge2$, $Sb < 5$) & 603 & 6.3 & Sect.~\ref{Sect:freqI}\\
           & II, III, IV ($N > 4, Sb < 5$)  & 225 & 11.1 (+2.7?) & Sect.~\ref{Sect:freqII}\\
Field KIII & (whatever $N\ge2$) & 5643$^a$ & 14.5$^b$& \citet{Famaey-2005}\\
           & Mermilliod \& Mayor (2007) ($N = 3$) & 285 & $16\pm2$ \\ 
Cluster KIII & Mermilliod \& Mayor (2007) ($N = 3$) & 704 & $30.8 \pm 1.7$ \\
\hline
\end{tabular}}
\medskip
$^a$ This number differs from the one quoted by \citet{Famaey-2005}, because we restrict the sample to stars having at least two radial-velocity measurements; $^b$~at the level Prob$(\chi^2(V{\rm r})) \le 0.001$.
\end{table}