I’m not going to lie to you; I previously had a post here about sex differences in cognitive abilities, focusing on intelligence. But I have since deleted it and started again, as I realize that I was wrong. Even a basic search of the scientific literature will show you that researchers are still divided on which sex has higher g-factor or IQ, the majority finds that there are no sex differences in intelligence, however, some find that males have higher intelligence on average.
I’ll just come out and say what I believe now: Males have a greater intelligence variance and a higher average IQ/g-factor than females – This causes males to be overly represented in the far right of intelligence normal distribution curve and in the end causes there to be more males in high societal positions, which require higher intelligence.
You may wonder why I came to that conclusion, especially since my previous post said that the intelligence of males and females was not statistically significant. Well, I reviewed the literature again and this time only based my conclusion upon the very high-quality studies, you will have to read on to gain a deeper understanding of what I mean.
Firstly, we need to talk about Richard Lynn and the Lynn hypothesis which, may or may not be correct (for the purpose of this article it doesn’t matter if it is right, only that it requires intelligence testing to be done on adults rather than children – just in case that it is correct.)
The Lynn Hypothesis-
The Lynn Hypothesis is a hypothesis developed by Richard Lynn , which states that females do have higher intelligence compared to males until they reach the age of about 16, where males overtake females. The reasons stated for this is that females mature earlier than boys, which explains why at younger ages they outperform males. This hypothesis appears to be supported by longitudinal studies  and studies at different ages  along with studies showing that females total brain size peaks earlier than boys.  Although there have been some contradictory results, for example . Lynn also provides a hypothetical reason for this disparity  One suggests that girls mature faster than boys because throughout human history there was mild polygamy, so females would have a reproductive advantage over other females if they could mature and reproduce early, where this would not be an advantage for males. An alternative hypothesis is that the female gamete deteriorates with age more than males so it would be best to breed as early as possible. These hypotheses have yet to be sufficiently proven though.
Because the Lynn hypothesis may exist it will be more meaningful to focus on any sex differences of intelligence in adult samples, rather than children. So that is what this article will focus on – Adult intelligence.
In response to the great amount of different studies collecting different results and a large amount of methodological problems which can affect results greatly, Nyborg created a 6-point quality scale, to get the best results possible. The scale was specifically designed to identify and existing sex differences and to reduce the effect errors have on the results.
The scale is quite simple  – One point is given to a study if the sample is representative. One point if there is a large number of tests (> 9). One point for diversity if it includes a wide variety of tests mapping obviously different abilities. Studies adding a Schmid-Leiman (1958) orthogonal rotation to the hierarchical solution are awarded another point. The application of a HFA analysis is awarded one point. One point is given if point-biserial correlations are calculated (including the interest correlation matrix before factor analysis and, finally, tested for significance after factoring.) No points are given for the inclusion of correlated vector analysis in sex difference studies for reasons explained in the original method.
Studies which score lower than 5-points are too untrustworthy to conclude anything.
Currently, there are only 2 studies which score high enough scores to base conclusions on. Them being (Nyborg, 2005  [N=62] ) and (Colom, 2002  [N=1,369] )
Nyborg found that there was a 3.15 IQ point male advantage, and also a greater variance for males than females. Colom’s study found male IQ advantage of 3.6 points in intelligence in general- but concluded there were no sex differences in general intelligence, this is because they did find a male advantage in g, but the value was combined with other sex-loaded g values that canceled out each other. However, it to Nyborg to do a statistical test of the observed sex load on g gives a highly significant male lead in g.
Thus, the highest quality studies have found a male advantage in g.
Moving towards studies with lesser methodological quality, but large sample sizes we find similar results. One study using SAT scores from 100,000 17 to 18-year-olds to measure g-factor found that males had an advantage of approximately 3.63 IQ points.  Another study of 3233 students found that in old adolescents (16-19 years old) males had an IQ advantage of 4.29, while in young adolescents (12-15 years old) there was only a 1.90 IQ gap in favour of males . However, there have been large studies showing the opposite result, for example, a study of 10,475 adult subjects showed negligable sex differences in intelligence 
It has long been known that men have larger brains than females on average, ranging from about 9 to 13% (not controlled for body size) , for example a study of 94 brains showed that the larger brain size in males meant that there were about 16% more neurones in the male neocortex, with body size having little effect . However, many believe that when controlled for body size that the sex differences in brain size disappear, this is not the case as only about 30% of the difference in brain size is down to body size differences. 
Combine this with the fact that there is a moderate correlation between brain size and IQ and g  and it should become apparent that, logically speaking, males should have a slight advantage when it comes to g-factor.
In response, some authors suggest that females could have greater neural packing density, however, this is contradicted by research. Research suggests  that there is no significant difference of neural density as well as the volume of neuropil, cells and blood vessels. There is, however, a statistically significant larger density of synaptic density in favor of males, not females.
There are two studies that I know of where the IQ advantage of males it calculated using brain size those being (Lynn, 1999 ) and (Nyborg, 2001, 2002, 2003 ). With Lynn finding a predicted IQ advantage of 4.05 and an observed one of 3.85, and Nyborg found predicted IQ advantage of 2.84 and an observed one of 3.15d. See table below.
These results support the idea that brain volume, at least in part, explains the sex differences in intelligence.
Greater male variance:
One thing which is not as debated is the fact that when it comes to intelligence males have a greater variance. For example, one study  in the USA which analysed 1292 pairs of opposite-sex siblings who participated in the US National Longitudinal Survey of Youth 1979 (male mean age for this experiment (SD) = 18.43 (2.07) years; female = 18.38 (2.08)), they measured g-factor (general intelligence) using Armed Services Vocational Aptitude Battery (ASVAB), from which the briefer Armed Forces Qualification Test (AFQT) scores were also derived.
The analysis showed that although males had a larger mean level of g the difference was marginal (less than 7% of a standard deviation- which is about 1 IQ point), the more interesting result is that males had a substantially greater variance. Among the top 2% AFQT scores, there were almost twice as many males as females, balanced by an excess at lower levels. Other studies have also shown this same thing.
Boys show this greater variance in intelligence at a young age (3 onwards).  However females have a higher IQ than males up to the age of 16 onwards when the opposite is true . Do keep in mind that all the above studies don’t score high on the 6-point quality scale, so should not be used to conclude anything about the mean difference in g, but it should be okay to use them as evidence of variability.
The Nyborg study showed a larger male variability compared to female as other studies, when it added the results from all ages of participants the standard deviation was 1.03 for males and 0.93 for females (N=181, Mean age=13). Using this variability (assuming a mean sex difference of 0) then there would be 2.4 times as many males at maximum right and left end of the g-factor bell curve than females.
What does it mean?-
Obviously, there is little to gain by looking at group means, as an advantage of about 3 or so IQ points is not enough to cause significant differences in large groups of people. The importance comes when you look at the very far end of g. However, even small changes in the mean would cause a great effect to the male to female ration at the very high ends of the normal distribution curve. And the larger male variance would increase the ratio at the far ends of the distribution.
The following graph is one I created, based upon the IQ difference in the (Colom, 2002) study (3.6 IQ points) and the Standard Deviation from the longitudinal (Lynn, 2004) study, (16.627 for males and 14.269 for females), I chose this study for the SD as it showed similar SD over all three chosen age ranges through three different IQ measures.
The results are striking. At the maximum score of 145 IQ points, there is a male to female ratio of 6.36 to 1.
When looking at the data college majors in the U.S and you plot the average IQ of each major and the percentage of the courses which are female a pattern starts to form (see figure below).
The amount of females in a course is negatively correlated to the average IQ of said course. Not just negatively correlated, but there is a strong correlation (r= -0.62633).
Females also make a minority of Nobel prize winners, out of the grand total of 885 Laureates only 49 were women . Of course, this could be influenced by social factors, never the less the gap is astounding.
Not only that but historical evidence suggests males make up about 98% of all the worlds accomplishments , again social factors are very likely influenced this (which makes it difficult to use historical data to prove something like this), also it could be that most of the accomplishments by females have been unrecognised, however even if we assume that 50% of all female accomplishments have been left out of the database (which is unlikely), that would still only mean 4.4% of all human accomplishments were down to females. The broad historical patterns in these data are not going to be changed even by implausible errors, let alone plausible ones.
All of this real world data supports the idea that there are more males at the far right end of the intelligence curve compared to females, and so males are more represented in achievements which require high or very high intelligence levels.
The results speak for themselves and they say that males have higher intelligence on average, along with greater variance, which leads there to be a large male to female ratio at the far-right end of the normal distribution curve. A conclusion which is supported by the highest quality studies and real world data.