Simon Baron-Cohen created the ideas of empathising and systematising, so I'd be wary of just assuming that these are generally accepted concepts which differ between men and women. The concepts are fairly close to the old arguments that women are emotional and men are rational.
In the paper which first reported these concepts, you can figure out that roughly around half the women tested (46% in one model specification, 51.5% in the other) did not actually seem to have what Baron-Cohen calls a female brain, but a balanced or a male brain.
The percentages of men who did not have a male brain were far lower (17% in one model specification, 40.4% in the other).
This could be because the questions he used might have been biased. The kinds of statements he lists in later sources as statements to agree or disagree with in the test look to me as if he puts systematising into the terms of male-coded professions, tasks, and hobbies, but doesn't really do the same for the assertions about empathising behaviour. There are many opportunities for exhibiting systematising behaviour within tasks, hobbies, and processions coded female, but those are not used in his tests. I believe that this biases the results.
Some examples for statements about systematising (I think these are from his book The Essential Difference or possibly from the test he offered to the general public around that time. My apologies for not writing down the source when I copied them):
- If I were buying a car, I would want to obtain specific information about its engine capacity.
- If there was a problem with the electrical wiring in my home, I'd be able to fix it myself.
11. I rarely read articles or Web pages about
new technology.
13. I am fascinated by how
machines work.
18. I find it difficult to understand instruction manuals for
putting appliances together.
25. If I had a collection (e.g. CDs,
coins, stamps), it would be highly organized.
29. When I read the newspaper, I am drawn to tables of information, such as
football scores or stock market indices.