The Washington Post reports: "Stereotypes of Quiet Men, Chatty Women Not Sound Science." Two new studies have shown that men and women actually tend to speak roughly the same amount of words per day. The difference is that they tend be more or less chatty in particular contexts. But overall, it balances out.
So, what is the root of the stereotype? My intuition is it is a classic (if more literal) case of "mistaking the sound of one's own voice for silence." I've developed this theory in relation to majority reactions to minority counter-discourse--the all-too-common claim that minorities now "dominate" conversations, that they are the truly privileged in social spaces, that their opinions are given enhanced weight. The data rarely bears these complaints out--most decision-making in America, especially at high levels, is done by White people listening to the advice and perspectives of other White people. But because that norm has existed for so long, the sound of White people talking feels like silence, and the unfamiliar voice of color appears to be a thundering imposition no matter how marginal it may remain to the overall schema.
I See Invisible People posits that people tend to over-estimate the amount of words spoken in conversations they are not interested in. I think that's true, but I'd go further. In this case, I suspect men see their own speech as important, meaningful, relevant, and significant, and so don't hear it as "speech" as much as necessary "activity." Women's speech, by contrast, is minimized as irrelevant, low-brow, gossipy, or idle, and thus extraneous. I believe what is actually being said via the stereotype that women talk more than men is that women talk more unnecessarily then men--the conversation stands out because it doesn't fit within the prevailing (male) paradigm of what counts as important speech. This, of course, is representative of gender hierarchy (i.e., patriarchy) more than anything else, and is thus interesting on that front, but there's not much there to be said that hasn't been already.
These conclusions are all just supposition. But just based on my observations and reading of related literature, I think there is more than an insignificant chance that it holds at least a grain of truth.