Standard Deviation

 

A.D.H.D.

Fuck that, eight doobies to the face
Fuck that, twelve bottles in the case nigga. Fuck that
Two pills and a half, wait nigga, fuck that.
Got a high tolerance when your age don't exist

And tolerance is where it’s at!

I would be lying if I said I understood anything that Kendrik Lamar said during the Super Bowl LIX halftime show. I don’t speak Rap. But Kendrick’s lyrics as quoted above are wise beyond words, The language is very rough, but….maybe I am merely showing my age. Tolerance is what engineers call Standard Deviation, the square root of variance. A problem is acting like mean and the midpoint of tolerance squared, variance, are the same. They are NOT, except for the absolute. There are three outcomes to any contest: win, lose, and tie. There is an average, mean of that contest. The average plus the tolerance should include the entirety. But because the mean, average, is defined as half of the absolute, it is confused that this requires that mean be constant, when it is NOT or the tolerance to be NOT constant, when it is. One is subject to growth, the average, and one is NOT subject to growth, the tolerance.

According to L’Hôpital’s rule, the limit of the average is the mean AND the median. But for anything less than the absolute, the mean and median can, and will, be different. The mean of an even number is half of that even number. The mean of an odd number is NOT an odd number, it is half of the original number, which makes it an even number. Thus saying the variance is one third of the absolute, while the location, is half of the absolute seems like it is a contradiction but the mean is subject to growth, and the variance is a constant and is NOT subject to growth.

Mathematically x>μ AND σ=μ/3 is true for the absolute but that does not mean that variance increases as the mean, location, increases. The variance is a constant, but the location can change with growth. The problem is that the limit of N/2, the mean, as N approaches the absolute is the absolute , but the limit of the Standard Error, what engineers call tolerance, the square root of the variance is SE=σ/√N, zero. This is true if the absolute is zero, but it is also true if the absolute is NOT zero, x>μ and σ=μ/3 is true not only for N=0, but it also is true for any value of the number N. There is no contradiction,  The mean is a function and changes. The tolerance is a constant and can NOT change. And apparently by not growing up in Compton like Lamar, I missed that.