For this exercise, I took pictures of white, grey and black card under natural light (overcast day). The three pictures came out almost the same, even though the three cards were of clearly distinct tones:
Out of the three photographs, only the grey card was correctly exposed. The white card picture was underexposed while the black one was overexposed. The camera was set in average metering and aperture priority mode with ISO set at the base level of 200. For the black card it selected a significantly lower shutter speed than for the white and grey ones. The histogram for all three pictures was almost the same: a relatively narrow curve in the middle of the tones, as depicted below
Switching now to manual mode, we took again all the pictures moving the exposure dial so that the histogram (in the camera) fell in the correct exposure section: The white card was overexposed (when compared with the aperture priority shot) so that its exposure curve fell entirely on the right hand side of the histogram (highlights), whereas the black card shot was underexposed so that the exposure curve moved to the left hand side of the histogram (shadows). The grey card shot was exposed so that the curve of the histogram fell in the middle:
There is a full stop difference between the white card and the black card correct exposure. The grey card exposure was actually about 1/3rd of stop slower than in aperture priority mode, but not too different from the correct exposure for the black card. Shooting at this speed would have likely resulted in the white card being underexposed. The more balanced exposure would have lied somewhere between 1/60s and 1/125s, as we will see next.
To understand a bit better how the camera works when presented with multiple tones at once (like in real life), I took a picture with half of the frame filled with white card and the other one filled with black card. The resulting picture is shown below:
On this occasion, the camera did a better job at calculating exposure, as the white section is closer to true white (but not there yet), while the black card section was closer to black (but still showing as dark grey). The histogram on this occasion had two separate peaks at the two extremes of the curve, but no values in the middle, which is consistent with the picture not showing any mid-tones. As anticipated, the exposure in this case is between the manual exposures for the white and black card, indicating that when the camera is confronted with a wide range of tones, none of which are particularly dominating, it is more likely to yield a reasonably correct exposure when used in average metering mode.