The other day i learned that depending on your mobile devices config, they can employ special power saving methods (maybe even when power-saving mode is off?), which are the cause for high latency and missed message notifications. Check out Proposal to change the default wifi beacon interval from 100 ms to 50 ms
Try to reproduce the ping values with laptop / computer device as client. That way, you will be able to eliminate any errors stemming from cell-phone usage. Also, scanning for wifi and using channel analysis at the same time while doing your ping-test will cause interference.