Is it common for 3rd gens cavaliers not ot have stabilizar bar on the control arm?. Some asked me if only some cavaliers had them?.

Thanks.

Yes - it is common for the "base" models to have come without a front stabilizer bar. I have a 2002 Sunfire SL, which did not come with one (as it was the cheapest model offered), but the next model up - the SLX did (and it included 15" wheels). On the Cavaliers here (Canada), those trims directly corresponded to VL and VLX.
This seemed to be common at least from 2000 to 2002 - I'm not sure about earlier years. In 2003, the stabilizer became standard equipment on all trim levels - even with 14" wheels.
John