Measuring the average frequency of signals
The weighted average "(sum over (fourier coefficient index * amplitude of that coefficient)) / number of fourier coefficients" does not seem very good as it will always give more weightage to the higher frequencies( because fourier coefficient index for higher frequencies will be higher) and the frequencies which you are looking for might be having low index. 

Better method could be to see which fourier coefficients have maximum values for each bang of hammer and corresponding to that you can find the major frequencies(band of frequency) for each bang. 

hope this helps.