MOSFET Basic Biasing Problems
You should look more closely at the data sheet. Go to page 2, and about the 3rd item is gate threshold voltage. This is defined as the gate drive necessary to produce 1 ma drain current, and is specified to be in the range of 0.8 to 3 volts, with a typical 2.0. 

In your breadboard circuit, in order to get Vcc/2 (5 volts) at the drain, you need 5 mA of drain current. Since a typical current at 2 volts is 1 mA, 5 mA at 2.4 volts seems perfectly reasonable. At voltages much below this the drain current will be right up next to 10 volts, since there is no current being drawn, and for much greater voltage the FET will be turned on hard and Vd will be near zero.

The only thing you really did wrong was computing gm. You seem to lost sight of the fact that this is your desired gm, not what you can actually expect. Go back to the data sheet, and you'll only find one gm value, specifically 0.2. However, notice the operating conditions - Vg is 10 volts and id is 250 mA, which is far, far away from the actual conditions you provided, so you can't trust it for what you were doing.