In 2012, the Canadian Olympic team sent 281 athletes to compete at the summer Olympics in London. The World Bank reports that Canada's population is approximately 34,000,000.
Using a raw analysis, you could say that, "A Canadian has a 281/34,000,000 probability of reaching the summer Olympics."
That is perfectly valid.
However, you cannot use that same technique to judge individual chances of success. Let's say that I am in a room with Brent Hayden.
Brent Hayden (a swimmer who won a bronze medal) is 6'4 and has a very athletic build. I am 25 pounds overweight, pasty faced from too much time in front of computers and completely void of hand-eye coordination.
Clearly, our individual odds of reaching the Olympics are different. The probability that I will make the summer Olympics is, in actuality, far below 281/34M because I am on the left side of the athletic prowess bell curve. Someone like Brent Hayden's probability of making the summer Olympics in, in actuality, higher than 281/34M because they would fall on the right side of the athletic prowess bell curve.
Those sorts of normal distributions happen in startups as well. Some teams are significantly more suited for the demands of startup lives (just like some couples are significantly better suited for the demands of marriage than others are).
So what you say with your example is that in a layered sample (say separate the population by heigh or muscle mass), the weighted mean is a better estimator than the arithmetic mean of a sample ?
In 2012, the Canadian Olympic team sent 281 athletes to compete at the summer Olympics in London. The World Bank reports that Canada's population is approximately 34,000,000.
Using a raw analysis, you could say that, "A Canadian has a 281/34,000,000 probability of reaching the summer Olympics." That is perfectly valid.
However, you cannot use that same technique to judge individual chances of success. Let's say that I am in a room with Brent Hayden.
Brent Hayden (a swimmer who won a bronze medal) is 6'4 and has a very athletic build. I am 25 pounds overweight, pasty faced from too much time in front of computers and completely void of hand-eye coordination.
Clearly, our individual odds of reaching the Olympics are different. The probability that I will make the summer Olympics is, in actuality, far below 281/34M because I am on the left side of the athletic prowess bell curve. Someone like Brent Hayden's probability of making the summer Olympics in, in actuality, higher than 281/34M because they would fall on the right side of the athletic prowess bell curve.
Those sorts of normal distributions happen in startups as well. Some teams are significantly more suited for the demands of startup lives (just like some couples are significantly better suited for the demands of marriage than others are).