Women may be making inroads into the tech and political realms, but when it comes to the corporate world, they have a lot of catching up to do--or rather, society does. That's according to a new Pew Research Center survey on women and leadership released Wednesday, which outlines just where they stand in the labor force. From making strides in managerial and professional roles to being more likely than young men to graduate from college (and continue learning), women are making real progress. Of course, there's clearly still room for improvement. Here are three takeaways from the illuminating study, guaranteed to get your office talking. 

Women: More Ambitious Than Men 

Though they continue to lag far behind men in the STEM industries of science, technology, engineering, and math, young women are more likely than young men to graduate college and outnumber men in college enrollment. In fact, Pew notes that by 2013, 37 percent of women ages 25 to 29 earned at least a bachelor's degree, compared with 30 percent of men in the same age range. Women also take advanced education more seriously, with 12 percent ages 25 to 34 in 2013 going on to earn a master's, doctorate, or professional degree, compared with 8 percent of men in the same age range. No wonder young women place a higher value on ambition than men--63 percent of millennial women tell Pew it's an essential leadership trait.  

Industry Stereotypes Run Deep 

The glass ceiling is still a very real thing, especially in corporate America, where it's rare to see women in top leadership positions. Currently only 26 Fortune 500 companies have women CEOs, comprising a paltry 5.2 percent of those leaders; the share of CEOs of Fortune 1000 companies is roughly the same (5.4 percent). Considering more Americans perceive women to have an edge over men when it comes to being honest and ethical (34 percent versus 3 percent), you would think the higher-ups would start reviewing their hiring practices. However, without giving reasons for it, the vast majority of adults surveyed feel businesses are not ready to put women in the C-Suite, despite their capacity. And the gender stereotypes really come out when the questions get industry-specific. Fifty-four percent of Americans say men trump women when it comes to leading professional sports teams and 46 percent say the same about running an oil and gas company. 

Women Have the Right Stuff 

Here's the good news: On several leadership traits, Americans see little distinction between men and women. Both genders prize intelligence and innovation and display those qualities equally. However, when it comes to compassion, organization, and honesty--all crucial leadership traits in their own right--distinctions emerge. For starters, 65 percent of adults say women are more compassionate than men, while only 2 percent say men show this trait more. Women are also perceived as being more organized (48 percent) and more honest (29 percent).