Series 2 of Doctor Who begins on the 15th of April 2006 and ends on the 8th of July the same year. In between two new things happen - we get a new Doctor (David Tennant) and he debuts in a Christmas Special, of which there will be at least one every year from now on (how can you have more than one Christmas Special? I refer you to 2009's end of year two-parter "The End of Time").
I have not included the Christmas Special in the above ratings, not only because it wasn't recorded as part of Series 2, it also wasn't broadcast as part of it. But here are the figures:
"The Christmas Invasion"
Overnights: 9.4 million. Finals: 9.84 million. Timeshift 4.5%.
As far as Series 2 goes, how does it compare to Series 1? Well the spread of viewers is pretty similar, with a peak at the start of the series. However as previously mentioned, viewing habits in the 21st Century are far removed from those of the '60s to '80s. You no longer have to choose between two conflicting broadcasts. The amount of viewers is no longer a measure of how much better or worse Doctor Who was than the opposition. Instead if you can now timeshift any programme you like, the only thing that determines whether or not you watch it is whether it was any good, not if it was better than what was on "the other side".
Comparing Series 2 to Series 1, we notice a slightly different spread of peaks and troughs. In particular, as in the early years of the Classic Series, viewers seem to be enticed back by things like Daleks and Cybermen. But what about the new Doctor? Introduced in "The Christmas Invasion" and allegedly the most popular Doctor since Tom Baker, you wouldn't believe it from David Tennant's first series. There's a couple of peaks over 9 million, but no episode reaches higher than this (whereas Series 1's "Rose" topped 10 million), and on average Series 2 (7.72 million) is slightly down on Series 1 (7.95).
And the Timeshift? About the same. 93.9% of viewers watch Doctor Who "on the night".