The second form of middle gray is from the average range of a scene. The statistically average scene has an luminance range of 2.20 logs or 7 1/3 from 100% R (0.0 RD) to 0.6% R (2.20 RD). The middle is 2.20/2 = 1.10 or 8%. If you round the scene to 7 stops, then the middle is 9%. This conforms with Jack Dunn's Exposure Manual. This can be thought of as the middle gray for the physical scene..
Ah, but 9% is the middle of the high and low - not the average of the distribution.