  We analyze the transit timing variations obtained by the Kepler mission for
22 sub-jovian planet pairs (17 published, 5 new) that lie close to mean motion
resonances. We find that the TTV phases for most of these pairs lie close to
zero, consistent with an eccentricity distribution that has a very low RMS
value of e ~ 0.01; but about a quarter of the pairs possess much higher
eccentricities, up to 0.1 - 0.4. For the low-eccentricity pairs, we are able to
statistically remove the effect of eccentricity to obtain planet masses from
TTV data. These masses, together with those measured by radial velocity, yield
a best fit mass-radius relation M~3 M_E (R/R_E). This corresponds to a constant
surface escape velocity of 20km/s.
  We separate the planets into two distinct groups, "mid-sized" (those greater
than 3 R_E), and "compact" (those smaller). All mid-sized planets are found to
be less dense than water and therefore contain extensive H/He envelopes, likely
comparable in mass to that of their cores. We argue that these planets have
been significantly sculpted by photoevaporation. Surprisingly, mid-sized
planets are discovered exclusively around stars more massive than 0.8 M_sun.
The compact planets, on the other hand, are often denser than water. Combining
our density measurements with those from radial velocity studies, we find that
hotter compact planets tend to be denser, with the hottest ones reaching rock
density. Moreover, hotter planets tend to be smaller in sizes. These results
can be explained if the compact planets are made of rocky cores overlaid with a
small amount of hydrogen, < 1% in mass, with water contributing little to their
masses or sizes. Photoevaporation has exposed bare rocky cores in cases of the
hottest planets. Our conclusion that these planets are likely not water-worlds
contrasts with some previous studies.
