PSD - Correct Formula for removing Noise Ok, so finally some things are making sense. 

I'm trying to scale the results, which I have done by the following equation:

$$
PS_{rms} = \frac{2 \cdot \left |y _{m} \right |^{2}}{
   S_{1}^{2} 
} m = 0.....N/2
$$

Where   $y_{m} = (re*re+im*im)$ 

This produces the following:



(Sorry about the axis - I have not had time to do these)

Prior to scaling the results, I got the following:



Essentially, so far, so good (I hope!)

Now I want to remove the noise around the signal, in theory, so that the main peaks are just showing and remove all the peaks that are not. So in theory, I would just be left between points (60 - 80).

I have been trying to read, and, understand the "Section 10: Averaging and overlapping" in this paper:
http://www.rssd.esa.int/SP/LISAPATHFINDER/docs/Data_Analysis/GH_FFT.pdf

It assumes that the usual remedy is to take the average of $M$ elements and reduce the standard deviation of the averaged result by a factor of $1 / \sqrt{M}$ however, what would be $M$ in this case? How could I therefore reduce the standard deviation, in order to remove noise from the result of scaling the PSD?

This is the only part to which I am now confused about, I essentially need to reduce the noise levels at the start of the result, and, at the end of the result thus giving me only the important peaks within the signal.
What you need is a digital filter. Digital filters are means to shape or "filter" the frequency response of a signal. Specifically, you need something called a band pass filter which would leave the 60-80 frequency mostly alone, and would mostly get rid of everything else. Snoop around this site or Google them. Digital filter are DSP 101, so there are many examples and tutorials out there.