Are you saying that Maobama would only have women in the less important lower paying jobs, I know for a fact he has several in cabinet levels, so why would an average work?
An average or a median comparison by gender doesn't work in situations like this, because women are overrepresented in low paying jobs, like secretarial work. In other words, there are likely to be far more women at the lowest paying end of the scale, as opposed to men. Not because of preferential treatment of men by Obama, but because of women making personal choices not to pursue degrees and/or taking lower-skilled jobs.
In order to do a valid study to examine female treatment in the obama whitehouse, you would have to eliminate personal choices made by those women which limited them to lower-paying jobs. The only sound way to look at this issue would be to compare men and women who have similar educational backgrounds and job titles. If the women earn less, there is bias.
But, when you compare secretaries to executive directors, you're not just looking at pay, you're looking at life choices (i.e., taking a lower stress hourly wage job so you can focus on family priorities), educational background, work experience, and work requirements.
This comparison is like comparing the salaries of every man who works in a hospital, on average, with every woman. You'd have more male doctors and many more female nurses, and that would skew things. You know the average doctor earns more than the average nurse...a lot more, in fact. The average department head makes a lot more than the average secretary. But, there are a lot of female secretaries in any sort of office setting...not because of discrimination per se, but because of selection bias...many more women choose to become secretaries, nurses, and teachers. Many more men choose to become firefighters, cops, security personnel, and construction workers.
You can't compare female secretaries to male doctors and come up with anything meaningful to talk about gender...the male doctor is worth more in the marketplace because of his degree and skills, not because he's male. The female secretary is worth less, not because of her gender, but because of her skills, education, and types of expertise.
It is what it is. Women with degrees tend to earn as much or more than their male peers. Women without degrees who do secretarial work don't even keep pace with their degreed female peers.
So, it probably went something like this:
Women:
20 secretaries
40 low-level staffers
30 mid-level staffers
20 high-level staffers
Men:
40 low level staffers
30 mid-level staffers
20 high-level staffers
The secretaries are going to pull the women's wages down to be artificially low because secretaries typically make a lot less than staffers.