We analyze the sample of measured nuclear magnitudes of the observed Jupiter family (JF) comets (taken as those with orbital periods P < 20 years and Tisserand parameters T > 2). We find a tendency of the measured nuclear magnitudes to be fainter as JF comets are observed with CCD detectors attached to medium- and large-size telescopes (e.g. Spacewatch Telescope). However, a few JF comets observed very far from the Sun (4-7 AU) show a wide dispersion of their derived absolute nuclear magnitudes which suggests that either these JF comets keep active all along the orbit, so the reported unusually bright distant magnitudes were strongly contaminated by a coma, or some of the measured ``nuclear magnitudes'' were grossly overestimated (i.e. their brightness underestimated). The cumulative mass distribution of JF comets is found to follow a power-law of index s = - 0.88 +/- 0.08, suggesting a distribution significantly steeper than that for both small main-belt asteroids and near-Earth asteroids. The cumulative mass distribution of JF comets with q < 2 AU tends to flatten for absolute (visual) nuclear magnitudes H_N &gt 16, which is probably due to incompleteness of discovery of fainter comets and/or a real scarcity of small comets due, perhaps, to much shorter physical lifetimes. In particular, no JF comets fainter than H_N ~ 19.5 are found in the sample, suggesting that the critical size for a comet to be still active may be of about 0.4 km radius for an assumed geometric albedo of 0.04. Possibly, smaller comet nuclei disintegrate very quickly into meteor streams. Most absolute nuclear magnitudes are found in the range 15-18, corresponding to nuclear radii in the range 0.8-3.3 km (for the same geometric albedo). We find that a large majority of JF comets with perihelion distances q > 2.5 AU are brighter than absolute nuclear magnitude H_N = 16, suggesting that only a very small fraction (a few percent) of the population of the JF comets with large q has so far been detected. A similar trend is noted for the corresponding absolute total magnitudes H_T taken from Kresák & Kresáková's (1994) catalog. By analyzing the H_N and H_T data, and trends in the discovery rate of JF comets as a function of their perihelion distances, the overall population of JF comets within Jupiter's region (q < 5.2 AU) up to an absolute nuclear magnitude H_N = 18.5 is estimated to be from several thousand to about 104 members. The q-distribution of JF comets shows a steep increase with q, which is consistent with JF comets coming from a flat intermediate source in the Jupiter-Saturn region.