I generated the figure at left from table 9.6 in The Genetics of Human Populations. This book was published in 1971, but I purchased the 1999 edition (which was simply a republication of the original text by Dover) in 2005.* At the time I recall reading the section on inferring the number of genetic loci implicated in the variation in pigmentation with some mild skepticism. The authors, L. L. Cavalli-Sforza and W. F. Bodmer pegged the black-white difference due to ~4 genes. Their data set consisted of individuals of various races in Liverpool; whites, blacks, people with one white parent and one black parent (F1 hybrids), people with three grandparents of one race and one of another ("backcrosses," where you take an F1 and mate them with one of the parental lines), and finally, F2 individuals who are the product of pairings of F1s.
To come to the estimate the authors made some assumptions. For example, they assumed that blacks and whites were disjoint on the genes which encoded skin color in terms of their variants. Because these two populations lay at the opposite poles of the phenotypic distribution for humans it's a natural assumption, but they had nothing to go on besides their hunch at the time. It turns out though that to a good first approximation this is actually a valid assumption. If you assume that the two populations are fixed at the allelic variants, that they don't have segregating alleles which encode variation, then whites and blacks should exhibit the same variance due to environmental forces. This is what the authors saw. Using skin reflectance measures it seems that blacks and whites varied the same amount about their mean. If the two populations are approximately homozygote then the F1 generation, which are heterozygotes, should be between the two parental populations in trait value, but not exhibit much greater variance. Recall that they'd inherit a black and white copy at every locus. Therefore, all the variance in this population should also be environmental, rather than genetic. The real action comes in the backcrosses and the F2 generation. In these two populations segregation will result in a genetic variance component which will inflate the total variance. Therefore, genetic variance on this trait can be estimated like so: