GPS has what is known as DOP or Dilution Of Precision. It means things aren't as accurate as you might want. There are 4 such values: TDOP, two HDOP values that are often merged, and VDOP. (Those are Time/Temporal, Horizontal, and Vertical. TDOP should be best, VDOP worst.) All DOPs are measured in meters, and ideally should be under 5. If you get both HDOPs, you should also get an orientation.
That your HDOP was 2 is actually quite good. This should be expected with a 9 satellite fix.
Velocity is NOT something GPS can tell you. But one can calculate it by taking the difference of successive readings. 19kph works out to 5.28 meters/second, or perhaps 0.53 meters/decisecond, if you are using a 10 reading/second device. This probably does indicate a certain amount of jumping around.
As for why it jumps: A big culprit can be partial cover. If you have the unit in a window, it could be partially blocked by the building (and HDOP tends to get highly directional in that case). Atmospheric conditions can mess things up. Nearby building could reflect signals. etc...