Do you know your uncle’s shoe size?
That’s what I was asked when I wanted to understand the “bell curve.”
What would your answer be to that question?
You might get confused with counter-questions like:
- Which uncle are you talking about?
- How would I know my uncle’s shoe size?
But surprisingly, my professor answered the question by the basic principle of the “bell curve.”
How a Bell Curve found my uncle’s shoe size?
He asked me further two more questions,
- What is the average height of an Indian? I answered 5.5 Feet.
- So, there is a high probability that your uncle’s height falls within the range of 5.5 feet, right? I said yes. –
And there is the answer, the shoe size of my uncle can fall under the average shoe size of a 5.5 Feet man.
But, what if my uncle’s height is 6 Feet? I asked him.
He said, – Yes! it could be, but the probability of your uncle being in 6 feet range is only a 16% chance.
I asked, How? – He unrolled the paper and draw a bell curve.
Say for example; If your uncle is in the age range of 40-50 years old, we take all the Indians and measure them. What we get is most of the population aged between 40-50 will have an average height of 5.5 Feet. Right?
I said, Yes!
Now, in the curve picture, we assume the center “0” value represents the 5.5 Feet. There the number of people in 5.5 feet will be higher than other hight so the middle line is taller than other lines.
I said, ok!
We take 0.5 Feet as the normal deviation from the 5.5 feet. That means some people will be shorter than 5.5 and some are taller than 5.5 feet. So, if we take how many people are shorter by 0.5 feet from 5.5 feet; that is 5.5 – 0.5 = 5 feet tall. We mark them at the “-1 point” of the curve.
Similarly, we place the taller people on the other side, like 5.5 + 0.5 = 6 feet. We mark them in +1 line.
[ Lets say, the -1 to +1 range is betwen 5 Ft to 6 ft, ]
- Sharpe Ratio
- Moderd Portfolio Theory