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Chances Are, I'm Smarter Than You
--------
by Chocolate Milk Enema
INTRODUCTION -- What I did in Stat class today.
------------
This is really such a fucking self-centered and self-aggrandizing
account, that you're just gonna HAVE to love me for it.
I was bored in my Statistics class today. This is nothing new. I'm
always bored in my Statistics class. Which might explain why I only go to
it once a week. On a good week.
So I calculated the probability that at least one other person in my
Stat class had an IQ either equal to or greater than my own. (Statistics
at work!) Actually, this took me most of the class to calculate, cause I
suck at statistics. I basically had to teach myself the technique.
Ultimately, I calculated this probability to be smaller than 0.0000003,
or less than 1 in 3.3 million. In fact, as the table in the back of my
Stat book was somewhat limited, it could even be as low as 1 in 30
million.
You can stop reading now. You know the punchline. On with the proof.
PREPARATION -- Goddamn I musta been bored.
-----------
If you have some background information in Statistics, it will help
you understand this. It will especially help you pick out the flaws in my
logic and calculations and therefore discredit me. If you have no
background whatsoever, none of this is gonna make any sense to you, which
will just make me appear even more intelligent, which will help you
accept my superior intelligence, with or without the proof, you pathetic
imbecile.
First we make some assumptions. Assumptions are the very BASIS for
the "science" of Statistics! All good statisticians know this!
Assume: My IQ is approximately 150. How do we know this? I took some
tests, asshole. Urine tests, yeah, but they do the trick; you just have
to know how to read the data and interpret the results.
Assume: The distribution of IQ's throughout the population of EARTH
is a normal distribution. Do you know what this means? Basically 95% of
the people on earth have "average" IQ's... say from 70 to 130. Of course
you must know that 100 is the mean average IQ. If your IQ is > 100,
you're one smart asshole. If it's less, you work at McDonald's, or a
subsidiary.
Now there's some REALLY SMART assholes and some REALLY DUMB assholes
at the extreme ends of the spectrum. These extremes make up a relatively
small percentage of the population: they're rare.
You'll have to take my word for this: approximately 1 in 1000 people
have IQ's of 145 - 160. This is genius status. Well, I read it somewhere,
so you don't HAVE to trust me. Go do some fucking research, smart-ass.
Even further up the scale, 1 in 10,000 will have an IQ greater than
160, and 1 in 100,000 greater than 175, and so on. Assuming this, the
chances that a randomly selected human being will have an IQ of 145
(approx 150) or greater is the sum of all these probabilities...
.001 + .0001 + .00001 + ..... etc.
For our purposes we'll use the value of .001111 just because we
don't want to work with any more decimal places. Why? Because we're lazy.
And frankly, it's not gonna make a whole hell of a lot of difference.
Okay. So we've assumed what MY IQ is and we've assumed what the
probability of being as incredibly intelligent (or moreso) as myself is.
This is already looking bad for you dumb assholes, isn't it?
HARDCORE MATH -- The part that breaks your brain.
-------------
Let's do some MATH!
First off, this is a binomial set of data. Any given statistic will
either succeed (be as smart or smarter than me) or will fail (dumber than
me!). P(success) [or p] = 0.001111 and P(failure) [or q] = 0.998889.
The size of the group [n] = approximately 70. I don't think there
are actually 70 people in the class, but it's close.
With 70 people in the class, and a probability of successes at
0.001111, you'd expect in an average random classroom to find
approximately 0.07777 individuals with my IQ or greater. This is the
expected mean. The standard deviation will be derived by:
/----------- (that's a square root sign,
sd = \/ n * p * q smart ass.)
sd is found to be = 2.7872.
We want to find the probability that x (the number of IQ's as high
or higher than mine) will be greater than 1. This is a binomial
distribution, which obviously means we can't have decimal values. x will
never be equal to 1.34 or 0.8. As such we have to consider round-off
error (or some Statistics jargon that means something sensible, anyway)
and therefore calculate the probability that x > 1.5. 1.5 is the
midpoint between 1 and 2: if greater than 1.5 the value would be 2. If
smaller, then 1. Therefore > 1.5 is actually 2 or more, which is what
we're looking for.
Here's some formulas I don't expect you to know. Back off.
P(x > 1.5) = P(z > (1.5 - 0.07777) / sd)
= P(z > 5.103) <-- this means 5.103 standard deviations
beyond the mean... VERY unlikely.
So I look at the table in the back of my Stat book, and it only goes
up to values where z = 5. We'll just use the value where z = 5, and keep
in mind that the actual probability is somewhat smaller.
At z = 5 the probability that a value will be to the left of z and
right of the mean is 0.4999997. A value will be to the left of the mean
the other half of the time, or 0.5. Add these two together to get
0.9999997 ... or the probability that x will NOT succeed.
1 - 0.9999997 = 0.0000003, or the probability that 2 or more people
in my class have my IQ or greater.
Therefore the chances are LESS than 1 in 3.3333 million.
CONSIDERATIONS -- I'm still a genius.
--------------
There may be some problems with these calculations. Obvious concerns
are that I just plain fucked up, cause I don't know shit. Hey, it's a
possibility, although a remote one. I wouldn't give it any merit
whatsoever.
Also, this is a university classroom. Now, you MAY want to assume
that the average IQ in a university is higher than say, just any old
place on your block like the bowling alley. (Of course, you may want to
assume the average IQ at the bowling alley is lower than most other
places, too.) Personally, I wouldn't give that much credence. People are
dumb all over. Especially in university. But, you know, maybe you're
right. Maybe Statistics 151 does attract the brightest and the best from
all around the world. Who knows.
In any case, I'm happy with this figure as a rough estimate. You
should be too. Or my big brain will crush you.
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