Abusing Statistics

February 12, 2007 at 7:53 pm | Posted in facts and figures | Leave a comment

Every one knows about the normal distribution. With a large enough sample/population, variations between people may be modelled with a normal distribution. Here I shall present a thought experiment

 

Purpose

To calculate the probablity of spotting an unusually unique member (in a positive manner) of the opposite sex while taking the MTR .

 

Theory

Beauty is in the eye of the beholder. Nevertheless, it is possible to relatively quantify it. Let us assume that appearances follow a normal distribution.

#####

Normal Distribution

-About 68% of values drawn from a standard normal distribution are within 1 standard deviation away from the mean; (the area under the curve between the two blue lines)
-about 95% of the values are within two standard deviations (the area under the curve between the two green lines)
-about 99.7% lie within 3 standard deviations (the area under the curve between the two purple lines)

 

normal_01.jpg

fig 1 – sketch of the normal distribution (by me)

#####

What can we say about the looks of people in general then?

-68% of the population (inside the blue lines) , within one SD, will be relatively “normal” looking

– then areas between the blue and green line represent (95-68 = 27) 27% of the population who are fairly pretty or beautiful (people can deviate positively or negatively, remember )

-between the green and purple lines are 4.7% of HK’s population, representing the very ugly/beautiful

-the tiny area outside the purple lines (0.3%) are the extreme pretty/not-so-pretty ones.

 

Everyone will have thier own perception of beauty, but the distibution/probabilites will be around the same.

because we are looking at unusaully desirable-to-look-at specimens of the hk population (and not the un-pretty ones), we divide the percentages above by 2.

-fairly: 13.5%

-very: 2.35%

-extremely : 0.15%

 

Now for HK’s statistics. I will assume that the age range in focus here be 15-34. You may debate with me on this point, but I’m being lax here.

#####

adding figures, we obtain:

% of population aged 15-34: 27.8% (using the latest statistics, mid-06)

 

 

#####

Derivation

Its all very simple. You have the percentage of people between 15-34. You have the percentage of people who are varying levels of “good-looking”. What else.

Let us assume that one can see all the peopl clearly half a carriage in front and half a carriage behind where you are standing in the MTR. i.e. – you can see 1 carriage’s worth of people, or 1/8th (0.125, or 12.5%) of the entire train.

Under normal not-so-crowded conditions, taken from my guesstimate in the “MTR ponderings” entry a few days ago, there would be around 88 people per carriage. Lets make it 100 for simplicity.

We can now calculate the probability that someone in your carriage on the MTR is fairly/very/extremely “pretty” in one trip.

-fairly: 13.5% x 27.8% x 12.5% = 0.469%

-very: 2.35% x 27.8% x 12.5% = 0.0869%

-extremely : 0.15% x 27.8% x 12.5% = 0.005%

these mean nothing. put into numbers (assuming 100 people per carriage)

-fairly: 0.469 people

-very: 0.0869 people

-extremely :0.005 people

Therefore, the number of people who are of the opposite sex in your carriage on the MTR who is fairly/very/extremely “pretty” per trip is:

-fairly: 0.235 people

-very: 0.0434 people

-extremely :0.003 people

Discussion

look! There is no level of beauty which is garunteed statistically. Thus you are not certain to see anyone pretty on the MTR every trip. There are some factors that I haven’t included.

-its not always the same bunch of people in one trip. People come and go. so the number of people per carriage would be greater. (yippee)

Lets say you take the MTR to and from school every working day of the week (mon-fri). What do we get? (twice every day for 5 days = x 10)

-fairly: 2.35 people

-very: 0.434 people

-extremely :0.03 people

Conclusion

There is hardly any chance that you will see a supermodel on the MTR, let alone talk to them.  Of course, if you happen to be bisexual, then your chances double. (not quite a good enough excuse to turn bisexual)

[edit: credit to Ykciv & Assosciates Law Firm for reminding me that I forgot to divide by 2 for males and females.]

ahahaha okay, thats enough.

News

Grammy awards [BBC news] was today. Apparently the Dixie chicks ran away with a lot (5 prizes). Other winners included Red hot Chili peppers (4) , Mary J. Bilge(3), Justin Timberlake…I’m lazy, lemme quote two paragraphs off BBC news:

Bruce Springsteen also won two awards, scooping best traditional folk album for We Shall Overcome – The Seeger Sessions and best long form video for Wings For Wheels: The Making of Born To Run.

Madonna picked up best dance/electronic album for Confessions On A Dance Floor, while Christina Aguilera, John Mayer and The Black Eyed Peas took home pop prizes.” -Harvard named it’s first female head in it’s 371 year history.

-Movenpick, the delicious (and [censored] expensive) ice-cream brand, now has chocolates out! they have 4 flavours. Here is one that I bought for around HK$21.00:

movenpick_01.jpg

whee…need to write up my last hmk, then I’m done for teh week (^^)v //

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