How to light a LED using photo transistors output?
Since you only care about deviations from recent "average", what you want is a high pass filter.  This also eliminates the large DC offset you have on your readings, and allows you to amplify the differences without amplifying this DC offset along with it.

You have to decide how long "average" takes.  In less hand waving terms, this means you have to decide which frequencies you care about deviations in, versus the frequencies you consider the "average" to be.  Once you decide that, you put a high pass filter in the signal path with a rolloff of frequency between the two ranges.

The rest is then deciding whether the variates are above some threshold or not.  This can be done with analog electronics, but doing this digitally in a microcontroller will take less parts, be more accurate, and provide greater flexibility in trying different things.  It also make it easier to produce a "changed" output that persists for some minimum time, perhaps some hysteresis, or whatever other non-linear manipulations might be useful for this particular instance.  You could even do gross high pass filtering externally, then more accurate high pass filtering at a higher frequency digitally.  Lot's of things are possible.