5th Sigma, 7th Sigma, 8th Sigma.......
A couple of guys were discussing about existence of 5th sigma and beyond and so I am writing my thoughts on it.There are a lot of things that exist but are not popular. Reasons for them being not to popular could be:
1. Not relevant or too marginal
2. The money of the world wants you to be a good little boy and not go beyond
Whatever.........
5th, 6th, 7th...........sigmas and beyond do exist. Take a look at this image I found:
The thing is that farther you go, the deviation just keeps getting smaller and smaller. For most industries going beyond 3 sigma becomes impracticable (because $). Those who go beyond are basically subscribing to more stringent guidelines. But mind you, rarely do they go to 5 sigma and sometimes they just loose steam at 4.5 sigma. Airline safety regulations compel aircraft engines to comply and take it to the next level - 6 sigma, but I am not too sure about that since standard deviation and a lot of statistical mathematics is used subjectively where industries are involved. You see with only a particular set of parameters taken into account, civil aerospace processes can reach 9 or even 10 sigma of tolerance. But when combined with other processes and the bigger picture is taken into account, it drops to 6 sigma levels.
Our concern is with this slope:
Before that gradient takes the slope of the line to zero (or horizontal to the surface) we will have some slope. So long as that gradient exists we will have numbers, which are theoretically unlimited and thus we can create as many slots out of them as we need. Therefore the 7 sigma and beyond.
Remember, I am not a mathematician. I just had too many semesters of mathematics ;-)
so funny math will always be my favorite subject :)
It is actually funny when you see the industry manipulating mathematical terms in order to push their products ;-)
yes they always offer more package less product and an a on special inflated price. The problem with that way of thinking is that it is based in the minimal or more with less sometimes it works and more often doesn't , trying to make the numbers say what they want you to believe, i'm not sure how many people on the planet even have enough education to understand the implications.
I think visually..so those graphs are great.
Next subject...what makes the bell tall and skinny or short and squatty.....and tails..
(mustn't forget the tails)
So as you would have already seen during your research, this is nothing but an idea of how far something is from the mean value. The Gaussian/normal distribution (or more practically the bell) is on a x-y plane.
So if we draw the distribution for a school test marks of a class, then x-axis could be the marks and y-axis would be the number of students.
In the above picture as you can see that students getting a 100/100 are in the far right (very few) and the students getting 0/100 are in the far left (very few) of the bell. Also most of the students have average marks of 60-65 and are in the middle (very high number).
This pattern indicates that most students would get marks closest to the average marks of the class. Students scoring very high or very low marks are fewer and fewer.
In this case the height indicates the number of students and the width indicate the marks they get. Thus a higher concentration of students near the median would make the bell taller and vice versa.
As for the tails. The slope gradually tapers of and flattens along the axis. Thus the distance of a point on the curve to the x-axis closes down to zero the further we move. This indicates a lower and lower chance of something/someone being there. Now since are date set is finite, i.e. even if one students gets a hundred or a zero the tail would never touch the axis.
For an ideal infinite data set, the tail would also not touch but would keep approaching a point where it might touch it. Thus the phrase - 'approaching zero' or 'tending to zero'.
The Gaussian/normal distribution (or more practically the bell) is on a x-y plane.
two dimensional....
just two.
OMG!....we're NOT flatlanders...
Oh...the realization of what this means is staggering.
Ha-ha. Sorry for making it sound so childish.
oh no..far from it.
it's been awhile. My brain hurts just looking at this haha
LOL! I know the feeling.
Excellent explanation.
Even I could (think) I understand it =)
Thanks man. I hope it was useful for you :-)