#### ApostateAbe

##### Banned

American blacks are many times more likely to drown than whites (http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6319a2.htm#tab), fulfilling the crude racial stereotype that "blacks can't swim." It could be just a cultural difference (fewer blacks have learned to swim therefore more drowning), but the physical data seems to have predictive power: blacks are more likely to drown due to different body densities. I will lay out the data and the math. Check the math, if you are so kind. I don't claim the math is infallible.

The study "Prediction of Body Density from Skinfolds in Black and White Young Men," (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1470565/) published in Human Biology in 1988, found that young white men have an average body density 1.065 g/mL, with a standard deviation of 0.012 g/mL, and young black men have an average body density of 1.075 g/ml, with a standard deviation of 0.015 g/mL. The difference in body densities may follow from a difference in bone density (http://ajcn.nutrition.org/content/71/6/1392.long), a difference in muscle mass (http://www.ncbi.nlm.nih.gov/pubmed/11505469), a difference in lung size (http://aje.oxfordjournals.org/content/160/9/893.full.pdf), or a combination of these differences. This would not be to imply that blacks have a selective disadvantage: the greater bone density of blacks may mean significantly less incidence of osteoporosis (http://www.ncbi.nlm.nih.gov/pubmed/21431462).

The average weight of a young man with the given densities per the study is about 80 kg or 175 lbs.

For an 80 kg black man, his volume is: 80 kg/(1.075 g/mL)= 74.4 L

For an 80 kg white man, his volume is: 80 kg/(1.065 g/mL)= 75.1 L

It is a difference of 0.7 L, or 0.7 L*(1.07 g/mL) = 750 g = 1.65 lb of extra buoyancy force for whites than for blacks.

So, the average black man in a swimming pool is like the average white man but wearing an extra 1.65 lb or gold chains (I choose gold chains for their very high density, not for the racial caricature). Doesn't seem like so much, but it makes a bigger difference when looking at the right tail ends of the body density distributions of each race.

Given a racial density difference of 0.01 g/mL, this means the average body densities of whites and blacks are about 0.83 white standard deviations apart and about 0.66 black standard deviations apart.

Using a z-score calculator (https://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html), assuming an extra weight of 1.65 lb, with z=0.66 black standard deviations, Q is 0.25, and it means that 75% of blacks are like the average white but with at least an extra 1.65 lb of gold chains. With z=0.83 white standard deviations, Q is 0.20, so only 20% of whites are like the average white with at least an extra 1.65 lb of gold chains.

Now we look at the right tail ends. What if it is a body density equal to an extra 5-pound weight of gold chains? For whites, this is 5 lb*(0.83 SD/1.65 lb)= 2.52 standard deviations above the white mean. This means Q is 0.005868, or 1 in 170. One in 170 whites have a body density equal to an extra 5-pound weight in gold chains. But, for blacks, this is 5 lb*(0.66 SD/1.65 lb)= 2 black standard deviations above the white mean and equal to 2 minus 0.66 black standard deviations equals 1.33 black standard deviations above the black mean. Another way to calculate this is that 5 pounds of extra weight for the average white is just 5-1.65=3.35 pounds of extra weight for the average black, and 3.35 lb*(0.66 bSD/1.65 lb) = 1.34 black standard deviations above the black mean. For z=1.34, this means Q is 0.090123 or 1 in 11.

So:

**1 in 11 black men is like the average white man but with an extra five-pound weight in gold chains, and this is 15 times as many blacks as whites**.

The amount of air in the lungs needed to compensate for five pounds worth of extra density is:

5 lb/(density of fluid) = 2.26 kg/(1 kg/L) = 2.3 L

So, 2.3 extra liters of air are needed to compensate for five extra pounds of gold chains. The extra air intake above normal intake from extra inhalation is 3.0 liters (IRV = 3.0 L per http://www12.homepage.villanova.edu/thomas.chubb/anatomy/S04/Measurements04.htm), an intermediate portion of which is typically necessary to achieve positive buoyancy, as all human bodies at rest are denser than water; without taking in an extra breath of air while swimming, you are more likely to sink. The 2.3 L is a significant cut.

Therefore, American blacks are much more likely to drown than American whites.

None of this is to claim that differences in average body density is the dominant explanation for any and all group differences. Differences in psychological swimming ability also have a significant effect, and they PROBABLY have an effect on the racial drowning differences. But, if there exists differences in psychological swimming ability between the races, then differences in average body density would likewise predict that, too: you are less likely to learn to swim if such learning is physically more difficult. And, regardless, any significance of such an explanation does not minimize the predictive power of the data concerning body densities and the physical predictions that follow.

So, how can this information be useful? Spot the drowning child.

Full story at The Daily Mail.