Coronal mass ejections (CMEs) may have major importance for planetary and stellar evolution. Stellar CME parameters, such as mass and velocity, have yet not been determined statistically. So far only a handful of stellar CMEs has been detected mainly on dMe stars using spectroscopic observations. We therefore aim for a statistical determination of CMEs of solar-like stars by using spectroscopic data from the ESO phase 3 and Polarbase archives. To identify stellar CMEs, we use the Doppler signal in optical spectral lines being a signature of erupting filaments that are closely correlated to CMEs. We investigate more than 3700h of on-source time of in total 425 dF-dK stars. We find no signatures of CMEs and only few flares. To explain this low level of activity, we derive upper limits for the non-detections of CMEs and compare those with empirically modelled CME rates. To explain the low number of detected flares, we adapt a flare power law derived from EUV data to the H{alpha} regime, yielding more realistic results for H{alpha} observations. In addition, we examine the detectability of flares from the stars by extracting Sun-as-a-star H{alpha} light curves. The extrapolated maximum numbers of observable CMEs are below the observationally determined upper limits, which indicates that the on-source times were mostly too short to detect stellar CMEs in H{alpha}. We conclude that these non-detections are related to observational biases in conjunction with a low level of activity of the investigated dF-dK stars.