Here is what Dr. Floyd Toole writes about Sound Power in his book:
"Sound power: is intended to represent all the sounds arriving at the listening position. It is the weighted average of all 70 measurements, with individual measurements weighted according to the portion of the spherical surface that they represent. Sound power is a measure of the total acoustical energy radiating through an imaginary spherical surface with the radius equal to the measurement distance. Thus, the on-axis curve has very low weighting because it is in the middle of other, closely adjacent measurement points (see the perspective sketch at the top of the figure), and measurements further off axis have higher weighting because of the larger surface area that is represented by each of those measurements. Ideally, such a measurement would be made at equally spaced points on the entire surface of the sphere, but this simplified spatial-sampling process turns out to be a very good approximation. The result could be expressed in acoustic watts, the true measure of sound power, but here it is left as a sound level, a frequency response curve having the same shape. This serves the present purposes more directly. Any bump that shows up in the other curves and persists through to this ultimate spatial average is a noteworthy resonance."