While I am certain there are circumstances where the disparity in pay is purely prejudice on the part of the employer, I am also certain that many statistics give a misleading figure.
For example sometimes when figuring the national average pay for a women they often include part time and stay home moms. I certainly make less than most men I know, considering I am a home mom. So I make zero for every dollar my husband makes. That doesn't appear to be the case in this survey as it said 'employed fulltime '
Also there is the demand factor. Many men are willing to go demand a higher salary while many women are often willing to accept the company’s policy of 3% cross the board wage.
And the statistics have difficulty taking into effect the actual job done. For example most wait staff at cheap restaurants are women, while most wait staff at very expensive restaurants are men. No judging her, just stating a fact. This leads to the theory that waitresses make less than waiters. But they are in different tip ranges.
Also many women are a bit altruistic, they are more willing to work in the poor rural communities, maybe being a doctor when the pay is often a bag of zucchini. Leading to the theory that all women Drs make less.
Specialization, women tend to gravitate away from specialization, prolly due to the genetics involved in being a good mother, good mothers can do it all

. But specialists make more money.
Or when a woman goes into a special field they do so knowing it well cost less to train them, which in turn leaves them with less income compared to a man, for example midwifery. I use a midwife because; well how on earth can a man know what labor is like anyway! But it is also cheaper. So my midwife gets less money than my ob-gyny would. Sorry. That goes along with the altruistic thing, Midwives could unite and decide to charge the same as ob-gyns, but that wouldn't be in the best interest of pregnant women.
There are many legitimate reasons for a woman to make less than a man. The serious cases of prejudice should be looked into, and punishment meted out, but the simple cases of a woman choosing to make less should not be used to fuel the fire.
In the case of not discussing employee pay, it is because then people would have reason to ask for more money, IE Joe makes x amount why don't I? Reason, Joe asked for x +5 but we negotiated down. If everyone knew what everyone made then employers would either have to put a stop to demand raises completely or give them cross the board, which one do you think a profit minded company is going to do?
In the case of that particular industry, please go look into filing an official complaint with HR, and then follow up. The government does take action if complaints are filed. Although you need a specific company, so say your looking at teachers you can't file a complaint with all schools, you need to go look school by school to see if there is a disparity. Then you need to ask every teacher if they asked for raises or not. Then file your complaint.