The discrepancy with the number in the article is that you're including 2^23 mantissae with exponent 0. In any case, the interesting bit is that half of floats are in the interval [-1, 1].
> the interesting bit is that half of floats are in the interval [-1, 1]
This is not so surprising once you realize that this just means you have the same precision for 1/x as for x, which makes a lot of sense for scientific calculations.
I'll clarify mostly for my sake (I hadn't thought about this before)
f(x) = 1/x takes takes numbers in the range (-1, 1) to numbers outside that range, and vice versa. The representable floats are split evenly between those two sets
One minor nitpick: f(x)=1/x maps [-1,1] to [-inf,-1]u[+1,+inf] ... that is, 1 and -1 are in both sets and mapped onto themselves. However, this detail doesn't affect the argument much.
