I'm right-handed, but I wouldn't put too much stock into this. If you're interested in historical statistics of mathematicians, read on.
First, it is not surprising (for cultural reasons) that up until the early 20th century, only three female mathematicians made a name for themselves: Sophie Germain, Sonya Kovalevskaya, and Emmy Noether. It will also not surprise anyone that so many mathematicians are Jewish: certainly Jacobi, Sylvester, Kronecker, Hadamard, Hausdorff, Noether, Lefschetz, Polya, Courant, Wiener, Zariski, and von Neumann. Outside of the major cities, Alsace-Lorraine has been a particularly good source of mathematicians (Poncelet, Liouville, Poincare) as has Silesia (Kummer, Kronecker, Hausdorff, Courant).
A lot of mathematicians came from quite well-to-do bourgeois, even wealthy, families, but the majority were of humble origins. On the whole, they move up substantially in the social class, as compared with their parents. This was particularly true in France, where to have attended one of the Grandes Ecoles confers social status, and to do so requires some depth of mathematical ability, especially in the case of the Ecole Polytechnique. About one quarter of great mathematicians, historically, remained unmarried.
When you look at the occupations of the fathers of major mathematicians, you find a great variety. Only three, those of Emmy Noether, Oswald Veblen, and Norbert Wiener, could be described as academics, and of those the last was not a scientist. Grassman, Galois, Mittag-Leffler, Hadamard, Hardy and Brouwer were the sons of schoolteachers; Euler, Abel, Riemann, Lie, E.H. Moore, and Borel were the sons of ministers; Kummer, Dedekind, Poincare, Birkhoff, and Aleksandrov were the sons of physicians; Poncelet, Cauchy, Hamilton, Henry Smith, Dedekind, Hilbert, and polya were the sons of lawyers. The fathers of Sophie Germain, Jacobi, Weyl, and von Neumann were bankers. Regrettably, a lot less is known about the mothers of mathematicians.
Not many mathematicians could be described as precocious, perhaps only Euler, Gauss, Abel, Jacobi, Hamilton, Galois, Poincare, Borel, Ramanujan, Winer, and von Neumann. The rare ability to recall vast quantities of data in a flash, or to perform huge calculations almost instantaneously, sometimes found in children, was possessed to a certain extent by some mathematicians, apparently Euler, Gauss, Hamilton, Poincare, Ramanujan, and Banach. However, it is debatable whether such abilities confer any advantage in higher mathematics.
Although the majority of mathematicians lived into old age, there are some who died while still in their prime. Consumption claimed Poisson, Abel, and Riemann, while Sophie Germain, Banach, and von Neumann died of cancer and Smith of a disease of the liver. Sophus Lie died, and Hilbert nearly died, of pernicious anaemia. Abel, Cantor, Sylvester, and Wiener showed signs of manic-depression, as is not uncommon in highly creative individuals. Outside Europe (with a vast majority from France and Germany), arguably only the United States, India, and Japan has had notable mathematicians until the early 20th century. To a large extent this is a reflection of the way mathematics has developed.