Here’s a replica of 5 lb. of fat and muscle. As you can see, the muscle tissue is more dense than the fat.
This is one reason I tell trainees (especially women) not to get too obsessed with weight–it can be deceiving. Adding some muscle is a good thing, but it may mean a less drastic change in one’s weight (especially in the first few weeks of training). In other words, gaining a few pounds of muscle and losing a few pounds of fat is progress, even when the number on the scale hasn’t changed very much.
A good program will include resistance training to build the muscle and help you lose fat (see: Weight Training and Weight Loss). Both goals are very important for transforming your body.