Hi, like some of the other putting stats, it can be a bit confusing.
It's simply because the Putting Avg. Per Round combines both your 9 and 18 hole rounds. It's pretty useless really, the Putting Avg. Per Hole is the important Stat.
To put it simply:
If you had a Putting Avg. Per Hole of 2 and only played 9 hole rounds, your Putting Avg. Per Round would be 18 (2 x 9)
If you only played 18 hole rounds, it would be 36 (2 x 18)
If you played 9 / 18 hole rounds equally it would be 27.
Hope that helps! Good luck.