My own anecdotal experience is that women tend to have far more friends than men do, and that that many of these are close friendships. Agnostic does not offer any data to contradict that perception.Skimming through facebook profiles, I get the sense that there is greater variation in the number of friends men have than there is in the number of friends women have. Variation tends to be more of a male characteristic, so this comes as little surprise. There are guys I play sports with who are high-energy, dominant alpha-types who have 2,000 facebook friends. That's way beyond the number of people they have actual personal relationships with, but they're approaching something like local fame in the number of people who are glad to be associated with them, and I'd wager that they tend to accept friendship requests more often than they request them. On the flip side, there are several guys I know from work who have fewer than 100 friends. Women seem more likely to fall in between.
The GSS doesn't offer much for us to play with here, but in 1986 it did query respondents on the number of close friends (excluding spouses and family members) they have. The mean is nine for men and six for women, while the median is five for men and four for women. In line with the unscientific facebook survey described above, the standard deviation for men is 12.7 for men and 9.1 for women. That is, men are more likely to have both no close friends and over ten close friends than women are.
GSS variables used: SEX, FRINUM