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Extracting and karyotyping XYY is pretty straight forward. The X0 Turner's syndrome (female) is similarly determined. XXY is Klinefelter's syndrome. It is mechanical observation. The presence of the genotypic expression as observed via the karyotype is not a guarantee of phenotypic expression. A phenotypic expression confirmed by examination of the karyotype would be unsurprising.

A description of typical XYY supermales gleaned from another web page:

On the average, these guys are taller have worse acne, have higher average hFSH, hLH, and testosterone (this has held up nicely), and allegedly average slightly lower IQ's (this point's very questionable), than XY's. These men average substantially higher testosterone levels, and are slightly over-represented in prison populations;
among tall men of any karyotype, the rate of conviction, especially for violent crimes, correlates surprisingly well with plasma testosterone levels, results of psychological tests correlate poorly with all these variables;
the typical XYY's crime is wife-beating;
the differences between XYY's and their XY counterparts are anything but striking.

OK, I haven't kept up with the literature like I should have. The IQ information is

The most dangerous creature on God's Green Earth is as follows: a man with a high IQ, high testosterone, a violently crackpot idea or two, an absolute certainty of his own righteousness, and an ability to turn on the "Reality Distortion Field" and inspire people to commit mayhem in his name.

Here is a strange question: If blacks have higher testosterone levels (10-20% higher) and blacks committ over 50% of the violent crimes...and higher testosterone is linked to higher propensities to crime...should they be punished less? These statisitcs are fascinating, if they are correct...but what implications can we draw for society from them? And what is the solution to "racial inequities" and "racial inequalities" if these inequalities are rooted in biology and not oppressive power structures?