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The McDonald Observatory Planetary Search program has been obtaining high precision ($\sigma \sim$ 10\,m\,s$^{-1}$) observations of a sample of 36 slowly rotating F, G, and K dwarfs since the fall of 1987. The primary purpose of this survey has been to detect sub-stellar companions to these stars. Most of the survey stars seem to have a level of intrinsic stellar radial velocity variability of about 20\,m\,s$^{-1}$ or less. However, the four stars of type F6 and earlier all seem to show significantly larger intrinsic variability of 40\,m\,s$^{-1}$ or more. These stars are $\pi^3$~Orionis (F6V), $\alpha$~Canis Minoris~A (F5IV-V), $\theta$~Ursae Majoris, and $\gamma$~Serpens. Stars of spectral type F8 and later do not seem to show this large level of radial velocity variability. One star of type F7V has recently been added to the survey, but we do not yet have sufficient data on it to determine its level of intrinsic variability. We present the observational data on these variable mid-F dwarfs, along with statistical analysis of the data in order to determine possible periodicities within the data. It is possible that these stars may represent the extreme ``tail end'' of the cool $\delta$~Scuti stars, or they may be a new class of variable stars in their own right.
