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We combined multi-wavelength data for blazars from the Roma-BZCAT catalog andanalyzed hundreds of X-ray spectra. We present the fluxes and Spectral EnergyDistributions (SEDs), in 12 frequency bands from radio to $\gamma$-rays, for afinal sample of 2214 blazars. Using a model-independent statistical approach,we looked for systematic trends in the SEDs; the most significant trendsinvolved the radio luminosities and X-ray spectral indices of the blazars. Weused a Principal Component Analysis (PCA), to determine the basis vectors ofthe blazar SEDs and, in order to maximize the size of the sample, imputedmissing fluxes using the K-nearest neighbors method. Using more than an orderof magnitude more data than was available when Fossati et al. (1997, 1998)first reported trends of SED shape with blazar luminosity, we confirmed theanti-correlation between radio luminosity and synchrotron peak frequency,although with greater scatter than was seen in the smaller sample. The sametrend can be seen between bolometric luminosity and synchrotron peak frequency.Finally, we used all available blazar data to determine an empirical SEDdescription that depends only on the radio luminosity at 1.4~GHz and theredshift. We verified that this statistically significant relation was not aresult of the luminosity-luminosity correlations that are natural influx-limited samples (i.e., where the correlation is actually caused by theredshift rather than the luminosity).

A Comprehensive Statistical Description of Radio-Through-$\gamma$-Ray Spectral Energy Distributions of All Known Blazars