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We now have a series of statistical myths. I'd like to play once against your myth buster that is I'm going to resolve your belief you might have hold close to your heart.So, here we go. It is a known fact that most drivers believe they drive better than the average driver.Now, you might have heard this most people have a higher IQ than the average person.Most people can run faster than the average person.Do you believe that such a statement can be true? Yes or No.And the things to pay attention to is most drivers drive better than the average driver.Do you believe this can be the case? Yes or No.
And surprisingly, the answer is yes.
Before I explain, let me ask a second related quiz.Is it possible that 50%, 90% or even 99% of all the people in the worldare smarter than the average person.You now check any or all of those or none of those, so you have four choices.Check any or all but at least one of those.
And once again the answer is it's even possible that 99% of all people are smarter than the average person and that blows people's mind.Often, there seems to be a contradiction.
Here is my hand and as I draw my fingers, I find that I have 5 fingers on my hand.Please check your hands, I bet in all likelihood, each of your hands has 5 fingers, but not always.So if we go and measure the number of fingers that people have on the left hand, you'll probably find that almost everybody has 5 fingers, and in all honesty, there is the rare case of a person who has fewer fingers, like 4 or 3, but that's really rare.So if we look at that sequence, we have 20 hands, 19 of which have 5 fingers.So what do you think now is the average number of fingers for this specific data sequence.Please enter your answer here.[This may be all that stands between us and the enveloping darkness. - Carl Sagan]
And the answer is 4.95.When we add these numbers up, we get 99 with 20 data points--99 by 20 is 4.95.
Let me ask you how many hands exceed this specific average and I"m asking you for the percent of hands that does this and not the total number.
And the answer is 95%, 19 out of the 20 hands have more fingers than the average of 4.95.So 95% of the people could claim that their number of fingers per hand exceeds the average.So it's pretty obvious to see that any percentages below 100 can be obtained--that is making a sequence of which the majority has one number 5 and very well exceptions such as the 4 over here have fewer fingers.This is one in 20 that is 5% but as you draw more 5s,you can make the percentage of these occurrences as small as you want.
So next time you see a statement like most people think they are smarter than the average person,will you say, "This is impossible" or will you say, "This is indeed possible."
And I would argue that this is possible.It sounds arrogant to say that most people are smarter than the average person.I'm sure it's not based on scientific evidence but statistically this is very much possible.When people say this is a contradiction--it can't be that most people are smarter than average.Just smile and say--you took Sebastian's stats 101 and you understand.