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In a histogram, mode
is the middle X value of the highest bar. (P3 in Diagram)
In a histogram of continuous distribution which function is unknown and smooth:
The modes are different from different interval settings in a distribution even the actual mode is one.
We develope the mode to find more reasonable and closer to the actual mode (Mp, peak of the curve) with
Tae Lee’s Mode = X3 + d/2 x (Y4-Y2) / (2Y3 -Y4 -Y2)
(Cut amending part off with ± 0.1d)
Pm(Xm,Ym), Pn(Xn,Yn) : (call the highest bar P3 among Pm...Pn)
d = X3-X2 = X4-X3 = interval
Conditions to use this formula:
- Ordinary unimodal distributions
- Y0>0, Y6>0, (Y2-Y1)>(Y3-Y2), (Y3-Y4)<(Y4-Y5)
Note :
- The above formula is based on the parabola which passes 3 points (P2, P3, and P4).
- With the same idea of above, the quartic function is applied with 5 points (P1~P5) in the computer.
- It finds more reasonable and reliable mode with checking the conditions.
- Free computer program is at the above Great Calc.
- This Mode Formula may not fit to find the peak of some curves.
But in the histogram of statics with measured data,
this formula finds better mode,
and reduces the errors come from various intervals.
- The 3 point Mode was developed in 1964, and the 5 point Mode in 2009.
Slide Rules Collection
- All the production of slide rules has ceased since the 1970's,
so there is no need to keep up with new models.
Therefore, even I, an extremely lazy man, was able to get into the collection of the
- Everlasting - Newest - Masterpieces - .
- Slide rule collection is not for everyone.
It requires some knowledge in order to understand the beauty of its system.
I was fortunate enough to come across these in my youth,
and invented the solution of Cubic Equations by using slide rules in 1966.
- For my collections, listed below, I selected the most technically advanced and useful slide rules
made by the leading manufacturers in the world.
25cm type (10inch)
Circular type
* Atlas and Binary have double cursors and 1610-D has a single cursor with a circular slide on either side.
Ref.: % Calculation Comparison
Each calculator has its own meaning regardless which is correct or better.
Isn't it funny that a simple math formula can have different meanings by ... ?
Actually many of the scientific calulators don't have "%".
Thanks. Tae S. Lee 
Suggestions or contacts: taelee@msn.com
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