The application of this problem is in bioinformatics, but the problem itself is a general math one, I think. I have a function that converts a sequence score to a value in time units. This function involves a logrithm, so it will of course be non-linear. I also have a sequence score for several different sequences, and I want to find the average.
I don't know whether to apply the function to each individual score, and then average all of those time values, or average the sequence scores, and then apply my function to that average. Both approaches give a different number, and I was hoping someone could tell me why one is obviously wrong.