  This paper is the second one in a series devoted to the study of properties
of binaries involving M giants. The binary frequency of field M giants is
derived and compared with the binary fraction of K giants. Diagrams of the
CORAVEL spectroscopic parameter Sb (measuring the average line-width) vs.
radial-velocity standard deviation for our samples are used to define
appropriate binarity criteria. These then serve to extract the binarity
fraction among the M giants. Comparison is made to earlier data on K giants
binarity frequency. The Sb parameter is discussed in relation to global stellar
parameters and the Sb vs. stellar radius relation is used to identify fast
rotators. We find that the spectroscopic binary detection rate among field M
giants, in a sample with a low number of velocity measurements (~2), unbiased
toward earlier known binaries, is 6.3%. This is less than half of the analogous
rate for field K giants, likely resulting from a real difference. This
difference originates in the greater difficulty of finding binaries among M
giants because of their smaller orbital velocity amplitudes and larger
intrinsic jitter and in the different distributions of K and M giants in the
eccentricity-period diagram. A larger detection rate was obtained in a smaller
M giant sample with more radial velocity measurements per object: 11.1%
confirmed plus 2.7% possible binaries. The CORAVEL spectroscopic parameter Sb
was found to correlate better with the stellar radius than with either
luminosity or effective temperature separately. Two outliers of the Sb vs.
stellar radius relation, HD 190658 and HD 219654, have been recognized as fast
rotators. The rotation is companion-induced, as both objects turn out to be
spectroscopic binaries.
