The news: Yahoo announced Marissa Mayer as its CEO in July, making her No. 20 on the list of female Fortune 500 CEOs.

Behind the news: Of the 32 Illinois-based companies on the 2012 Fortune 500 list, only three are led by women: Ilene Gordon of Corn Products International, Irene Rosenfeld of Kraft Foods and Patricia Woertz of Archer Daniels Midland.

In 2010, women comprised 50.8 percent of the population and 47.1 percent of the labor force in Illinois, according to the U.S. Census Bureau’s 2006-10 American Community Survey.

But they covered about 28 percent of “senior level/executive or manager positions” in 2010, according to the U.S. Equal Employment Opportunity Commission.

Nationwide, a 2011 study of the S&P Composite 1500 companies by American Economic Review found that women accounted for 47 percent of the overall workforce from 1997 to 2009 but held only 6 percent of corporate CEO and executive roles.

David Matsa, the study’s co-author who is an assistant professor of finance at the Kellogg School of Management at Northwestern University, said that there’s a connection between a company’s makeup at the executive level and the number of females in positions of power.

“When there are more women holding seats on boards, there is an increase in the amount of females within a company and in top positions,” he said. “Women are certainly each other’s best advocates, and it does matter who is hiring.”