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. 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, then she was born in 1925.
However, Rowling's writing about McGonagall on Pottermore indicates that she changed her mind about the year of McGongall's birth. She states:
Though a most efficient and gifted employee, and fond of her much older boss, Elphinstone Urquart, Minerva was unhappy in London, and found that she missed Scotland. Finally, after two years at the Ministry, she was offered a prestigious promotion, yet found herself turning it down. She sent an owl to Hogwarts, asking whether she might be considered for a teaching post. The owl returned within hours, offering her a job in the Transfiguration department, under Head of Department, Albus Dumbledore (Pm).
When did this happen? According to McGonagall's conversation with Umbridge:
"How long have you been teaching at Hogwarts?" Professor Umbridge asked.
"Thirty-nine years this December," said Professor McGonagall brusquely, snapping her bag shut.
This conversation happened on September 10, 1995, which means that McGongall started teaching in December of 1956. Counting back the two years indicated in Pm tells us that she left school in July 1954. Therefore McGonagall was born on October 4, 1935, and started Hogwarts in 1947, aged 11 years, 11 months.
So what about the reference from the Sch2 interview? Well, that's tertiary level canon, and is therefore trumped by subsequent secondary canon (Pm) and primary canon (OP) references.