How to calculate the entropy of a file?

Question

How to calculate the entropy of a file? (Or let\'s just say a bunch of bytes)
I have an idea, but I\'m not sure that it\'s mathematically correct.

My id

Answer 1

A simpler solution: gzip the file. Use the ratio of file sizes: (size-of-gzipped)/(size-of-original) as measure of randomness (i.e. entropy).

This method doesn't give you the exact absolute value of entropy (because gzip is not an "ideal" compressor), but it's good enough if you need to compare entropy of different sources.