Math, Statistics, and Sex

So I heard an interesting statistic being discussed on the news.  Supposedly an extensive survey found that in America the average number of heterosexual partners for a male is significantly higher than the number for a female.  They concluded that this is due to cultural pressure that identifies promiscuous males positively as "studs" while portraying promiscuous women negatively, as "sluts."  That is unfortunately not the correct explanation for the numbers they found.  The correct explanation is that one group or the other is exaggerating/lying, and this is easy to prove mathematically.

If we assume there are an equal number of males and females in the US, (The slight actual difference in the US is insignificant, but the only way for the averages to differ.) and remove same sex partners from the equation, the average number of partners will always be the same for both genders.  Every time two people sleep together for the first time, that adds one more to the total number of unique partners for both genders.  Even if one guy sleeps with ten girls, as long as there is an equal number of each gender in the sample pool, the average will always be exactly the same. (There must be nine other guys who hadn't seen any action in that case, and even if they had, it would have increased the female total by the same amount.)  The median may be different, but the average will always be the same.  Even if you factor in the weird cases, like if a guy sleeps with two girls at once, that adds two to his count, and one to each of theirs, for a total of two as well.  If you add up all of the partners that the members of one gender have slept with and divide by the total number of members of that gender, you will get an average.  All total numbers will be exactly the same for the other gender, and the average will always be exactly the same.  So a small difference can be attributed to anomalies from a limited sample size, but a significant difference must be attributed to inaccurate reporting by people about their experiences.  Now that lying or exaggeration might be attributable to those cultural perceptions about “studs and sluts,” but the actual numbers in reality will not reflect any results of that possible perception.

In China on the other hand, where there are many more males than females, due to gender selective abortions, the averages WILL be different.  If there are twice a many males than females, females will on average, have twice as many sexual partners as the guys will.  Although this appears to assume that the females will have to be more promiscuous for that to take place, that is not true.  The total number of partners will be the same for both genders (assuming no international relationships) because every new "union" always adds one to the total for both genders.  This is then divided by the total number of members of that gender.  If there are more of one gender, like twice as many guys, that will cut their average in half.  This is easy to visualize with a pool of just two guys and one girl.  Whether she sleeps with one or both, her average number of partners will be twice theirs.

So we can see that comparing the average number of partners between genders tells us absolutely nothing, because any true difference would merely reflect a difference in the number of each gender, not on their behavior. (Average number of partners, regardless of gender, is the only meaningful number that could be derived from this study.)  But somehow no one seems to notice that mathematical reality, and this study ends up making it into the national news, and discussed as if it actually reflects a gender issue in our society.  (And now you know what I ponder for the next few hours, when I hear something that ridiculous on the news while traveling, and don't have anything else to do for a while.)