Her father, Robert McGonagall, is a Muggle and a Presbyterian minister. Her mother, Isobel McGonagall, is a witch. They name her after Isobel’s grandmother, who was a skilled witch. (Pm)
JKR said in Sch2 that McGonagall was "a sprightly 70" years old. Using that information, we can determine the year in which she was born by subtracting 70 years. As with Dumbledore's birthyear, the trick, of course, is knowing what year to subtract that 70 years from. If we assume that Rowling was saying that McGonagall was 70 years old at that point in the stories, which was summer of 1995 [Y15], then she was born in Y-55 (Y15 minus 70 years). According to the official timeline, Y-55 is 1925. Interestingly, that would make McGonagall a contemporary of Tom Marvolo Riddle at Hogwarts...
October 4 comes from JKR.
original artwork Â© 2001 Laura Freeman, used by permission