The DC bin of an FFT should be the mean of all the other bins in the spectrum, why does the FFT produce 0? I am experimenting a bit with FFT's. From what I have read the first bin of an FFT is called the DC bin -- that is it is the mean of the other components in the FFT. I have also read that it should be close to 0.

When I actually perform the FFT and take the absolute value, what I find is that the first element of this is always 0. This makes sense mathematically if you consider the definition of the DFT itself.

Is there a best practice to reconstructing this first DC bin? 



So it seems that because I was making my test FFT with a sine wave as the transient signal, this is what caused the 0 valued first FFT bin. I changed it to a cosine and got a non-zero first element...And the same with any random data. I should have thought a bit first.
Depending on your normalization factor the DC bin is either the sum of the signal values in your frame (1), the average (1/N), a "representation" (1/sqr(N)),

In the DFT formula the exponential value is $e^0$, or 1, for each term.