For a school project, I need to know how to gather statistical and numerical data by analyzing compressed digital audio formats like mp3's from its lossless version. I basically need to know how to gather data in terms of fidelity from a lossless to lossy format. Are there any programs, or a method to understand wave graphs/spectrograms that can help?

First things first:

Spectograms and numerical difference between waves do not represent good and/or reliable data for lossy quality evaluation.


Next:

The usual way to evaluate lossy codecs is by use of human-conducted tests (ABX and ABC-HR are two of those methods). This involves getting different samples and different people to test/rate them.


At last:
There are some programs that try to evaluate the codecs in a similar fashion that human-conducted tests would run. EAQUAL is one such programs.
These programs are limited by the fact that they use the same or very similar methods to check the audio data than the lossy codecs use themselves, so In the end, it is a cat-&-mouse game between who gets the best results.

Most lossy encoding is perceptual encoding, which means the loss is only what is inaudible to (not perceived by) normal human hearing. The measure of its quality is how well it does that, i.e. how close to the original the encoded audio sounds when a human listens to it. Measures of data differences are not relevant. A relatively large amount of data difference (quantity) might still produce an inaudible difference, thus very high quality, depending upon the encoder and the particular audio input.