A couple comments.
First, the voting thing brings to mind a couple of thoughts.
We are essentially putting people into statistical bins and comparing participation between bins. The problem with this is that it's not that simple. You can't put people in single factor bins (like race) and then make comparisons. There are other factors as well: income level, education level, urban/rural, neighborhood, etc. It is necessary to to a more in-depth analysis to determine which factor is the real correlation and which are incidental correlations due to the difference in the population make-up within the bins of that factor.
As illustration (assuming this isn't more than I'm allowed to quote):
http://www.fairvote.org/what_affects_voter_turnout_rates
Demographics: In the aggregate, voters tend to be older, wealthier, more educated and whiter than non-voters.
Age: Young people are much less likely to vote than older ones. From 1972 to 2012, citizens 18-29 years old turned out at a rate 15 to 20 points lower than citizens 30 year and older.
Race/ethnicity: Voter turnout also varies by race and ethnicity. In 2012, turnout rates among eligible white and black voters was 64.1% and 66.2%, respectively, while it was only 48.0% and 47.3% among Latino and Asian American voters respectively. The 2012 election was the first presidential election since Reconstruction ended in which black turnout exceeded white turnout.
Gender: Women's voter turnout has surpassed men's in every presidential election since 1980. In the 2012 election, 7.8 more women than men voted. Interestingly though, older women are actually less like to vote than older men. In 2008, 72.2% of men 75 years and older voted, compared to only 64.9% of women that age.
Socio-economic status: Wealthy Americans vote at much higher rates than those of lower socio-economic status. During the 2008 presidential election, only 41% of eligible voters making less than $15,000 a year voted, compared to 78% of those making $150,000 a year or more. Studies have shown that this difference in turnout affects public policy: politicians are more likely to respond to the desires of their wealthy constituents than of their poorer constituents, in part because more of their wealthy constituents vote.
This can extend to qualifications. Should expected representation be based on representation of the minority in the overall population or in the population of qualified persons? My daughter is studying personal fitness training. Most of her class is men. So due to qualifications, you cannot reasonably expect 50% of applicants for a PFT job to be female.
Even if the number of certified PFTs were equal, there are other issues, based on observations she has made in class. My daughter is athletic. She was a softball pitcher and cheerleader in high school and played volleyball in middle school. But she is at a significant disadvantage over her male classmates, because she doesn't have the same strength that the men do. The consequence of this, from a professional standpoint, is that it is difficult for her to spot for men lifting heavier weights. Consequently, when she gets out in the workforce, she will be limited as to which clients she can work with. So from a hiring perspective, a gym owner has some considerations to make. A male trainer is going to be more versatile because they can safely work with a larger portion of the clientele. (Also, many clients will be more confident in their safety being spotted by a male.) Of course, there is a benefit to having female trainers on staff as well, because some women may be more comfortable with a female trainer. But does it make sense to staff at a 50/50 male female split? Probably not. And note, that the hiring here is really not based on gender, but on the physical abilities that happen to favor one gender over another.
Now, construction/carpentry jobs have been mentioned previously in this thread. Are women less interested in this work for cultural reasons or is it because of physical differences. Are male bodies in general more suited to repeated tasks requiring upper body strength over the course of the day? Might women not gravitate to those fields because the work is more stressful on them than it is men? I'm not sure, but it is a reasonable possibility that should be investigated before pointing out under-representation. It just might be a harder job for women than men making it less attractive.
I could go further with some speculation on how construction being unattractive could divert someone from related fields like engineering, crane operator, etc. But that's just speculation.
