Abstract: In this paper, to study the physical properties of blazars, we collect a large sample of Fermi blazars with (quasi) simultaneous data and well fitted spectral energy distribution. We analyze five correlations for the whole sample, the FSRQs only and the BL Lacs only, respectively. Our main results are as follows. (1) We find that there are significant anti-correlations between the synchrotron peak frequency and the synchrotron peak luminosity, between the inverse Compton peak frequency and the inverse Compton peak luminosity, between the synchrotron peak frequency and the bolometric luminosity for the whole sample, but no correlations for FSRQs and BL Lacs. There are significant anti-correlations between the synchrotron peak frequency and the Compton Dominance for the whole sample and BL Lacs, but no correlation for FSRQs. There are significant anti-correlations between the inverse Compton peak frequency and gamma-ray spectral index for the whole sample, the FSRQs only and the BL Lacs only, respectively. (2) One cannot exclude the possibility that the above correlations for the whole sample are affected by the difference in distribution of FSRQs and BL Lacs in the parametric plane. (3) We suggest that the significant anti-correlation between the synchrotron peak frequency and the Compton Dominance for BL Lacs may provide an evidence for a fast-cooling emission mechanism for BL Lacs. (4) The anti-correlations between the inverse Compton peak frequency and gamma-ray spectral index provide an observational information to the leptonic jet emission model with a log-parabolic shaped electro energy distribution (EED).