The solar corona produces coronal rain, hundreds of times colder and denser material than the surroundings. Coronal rain is known to be deeply linked to coronal heating, but its origin, dynamics, and morphology are still not well understood. The leading theory for its origin is thermal instability (TI) occurring in coronal loops in a state of thermal nonequilibrium (TNE), the TNE-TI scenario. Under steady heating conditions, TNE-TI repeats in cycles, leading to long-period EUV intensity pulsations and periodic coronal rain. In this study, we investigate coronal rain on the large spatial scales of an active region (AR) and over the long temporal scales of EUV intensity pulsations to elucidate its distribution at such scales. We conduct a statistical study of coronal rain observed over an AR off limb with Interface Region Imaging Spectrograph and Solar Dynamics Observatory imaging data, spanning chromospheric to transition region (TR) temperatures. The rain is widespread across the AR, irrespective of the loop inclination, and with minimal variation over the 5.45 hr duration of the observation. Most rain has a downward (87.5%) trajectory; however, upward motions (12.5%) are also ubiquitous. The rain dynamics are similar over the observed temperature range, suggesting that the TR emission and chromospheric emission are colocated on average. The average clump widths and lengths are similar in the SJI channels and wider in the AIA 304 Å channel. We find ubiquitous long-period EUV intensity pulsations in the AR. Short-term periodicity is found (16 minutes) linked to the rain appearance, which constitutes a challenge to explain under the TNE-TI scenario.