Are males taller than females in humans?
Are males taller than females?

Best data I could find come from the Statistical Abstract of the United States (1999) > Section 3. Here is a table reporting the percentage of the male and female population which height is lower than a given threshold



Note that this data collection was done among students in US universities and is therefore not representative of the whole world or even the whole country.

Does height follow a bimodal distribution?

A difference in height between males and females is often used as a classical example in introductory statistic class to exemplify a bimodal distribution as seen in this picture



and on these (a priori fake) data



However, Schilling et al. 2002 argued that while the difference in mean height between the sexes is real, this difference is too small relative to the variance in height within each sex to be clearly depicted on a graph.

Note that I found this non-peer-reviewed paper which shows real data that display a truly bimodal distribution of height.



Genetics of height

The question why are they taller? is very broad. I will just focus to give you some hints about the genetics of height in humans. First, you want to make sure you understand the concept of heritability.

Evoy and Vissher 2009 report a heritability coefficient of 0.8. This estimate is impressively high - only a few phenotypic traits have such high heritability. They also review articles discussing that 50 loci are correlated with variation in height (actually, today, more than 500 loci are known to contribute to height, see the link in AlexDeLarge's comment to this answer). However, these loci are not sufficient to explain the whole heritability observed (common missing heritability issue). Yang et al. 2010 provide evidence that the remaining heritability is due to incomplete linkage
disequilibrium between causal variants and loci of weak effects. In short, height is a highly polygenic trait.

Related post

You should have a look at Is there a genetic reason explaining the difference of the height of male and female? for more information.