MENSA is for people who score above the 98th percentile on accredited IQ tests.
98% of people who are eligible don't join.
98% of MENSA members don't join until the're older and have exhausted every other means of making friends.
98% of parents wouldn't sign their obviously advanced kid up at an age where she has no sense of the sheer nerditude involved.
Quick, Brainiac, what're the odds ofa 2-yo joining?
Answer: 1/0.02^4, or 1 in 6,250,000.
Which is funny, because when 2.75-yo Hampshire UK [ed note: Old Hampshire?] toddler Georga Brown's parents signed her up, after taking her for an IQ test, they found out she was only the second youngest member in the group's history.
"The youngest ever member was a boy, who was several days younger than Georgia when he joined in the 1990s."
Britain's birthrate: about 650-670,000 babies/year.
Girl, 2, becomes member of Mensa [bbc.co.uk]