The extragalactic radio sources are divided into two subclasses (radio-loud and radio-quiet sources) in the literature using radio loudness (R), which is defined as the ratio of radio emission to optical emission, but the boundary R-value separating the two classes is different in various sources. In this work, a sample of 2419 objects from the 13th catalog of quasars and active nuclei is used to build a boundary for the two subclasses. To do so, we compiled the radio and optical data, calculated their radio and optical indexes, made K-correction, obtained the radio loudness, and adopted a Bayesian analysis method to the logarithm of radio loudness for classification. We also investigated the correlations of radio loudness with radio/optical luminosities. Our main conclusions are summarized as follows: (1) The distribution of the logarithm of radio loudness (log R) is bimodal, the sources with log R<1.26 are classified as radio-quiet sources, and those with log R>1.26 are classified as radio-loud ones from the Bayesian analysis method. (2) The average radio-optical effective spectral index of radio-quiet sources is <RO>=0.05, while that of radio-loud sources is <{alpha}_RO_>=0.55. (3) There are positive correlations between radio luminosity and radio loudness for both radio-loud sources and radio-quiet sources. (4) A dividing line of separating the distribution of the clusters on the diagram of radio loudness against radio luminosity was obtained statistically to set the boundary between radio-loud sources and radio-quiet sources, with an accuracy of 99.73% based on the classification result from the Bayesian analysis method.