Statistical Trigonometry Vs 3 Standard deviations
Statistical Bell curve Vs 3 Standard Deviations:
Statisticians are aware that most of the times the bell curve is based on the grounds of three standard deviations. The question been asked by myself that why is it going to be only 3 standard deviation to design a perfect bell curve. For few days, I thought it might be just a basic to say its only 3 standard deviation because we have been taught so.
However, saying that it has been taught so is a wrong assumption to define it. In addition, my idea turn to Phi, which is equivalent to 3.2 in order to define the perfect bell curve, which touches to the basement of 3.2. Still not satisfied.
I turn to trigonometry and I find a satisfying answer being asked by myself and getting the solution out of it. I took a triangle and draw parallel to the bell curve and find out the 3 axes to it i.e. A, B, C (Triangle) = 1, 2, 3 as defined in the below diagrams. We are setting the standards to the curve in order to set the mathematical solution to the curve, which is parallel to find out the gaps between the axes.
It defines how close is our stats with trigonometry and being used on the practical grounds of 3 standard deviation (Bell curve) vs the triangle (Trigonometry)
The triangle defines having 3 zones which is equivalent to the 3 standard deviations for a bell curve in order to perfect the statistical analysis.
On applying the total view of a triangle into bell curve defines the following shape in real on the grounds of setting the standard deviation to 3.
Real time data :
Using 3 Standard deviations for a sample is the best practice in order to measure the correct sensibility and right measurements for the data on the grounds of mathematical judgments.
Measuring the data on the grounds of 4 Std is not satisfactory because the triangle have 3 phases, same which matches to the curve deviations. If it is a square yes we can apply 4 deviations on the grounds of square to apply mathematically into statistical analysis.
Application of 4 Std will be coming into my next posts as a new concept of applying a square into 4 std concept which still have 3 std for a square concept zone (Trigonometry).
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