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  Tae Lee's Mode

  in histogram of statistics
    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)

    #
        maker
        model
    country
      rules
    upper body slide lower body
    1
    Nestler
    0292
    Germany
    28
    LL00-LL01-LL02-LL03, DF
    P, S, T1-T2, A
    [CF, CIF, CI, C]
    [B, K, CI, C]
    D, LL3-LL2-LL1-LL0
    D, R1-R2, L, ST
    2
    F.&Castell
    2/83N
    Germany
    31
    T1-T2, K, A, DF
    LL03-LL02-LL01-LL00, W2
    [CF, B, CIF, CI, C]
    [W2', CI, L, C, W1']
    D, DI, S, ST, P
    W1, D, LL0-LL1-LL2-LL3
    3
    Aristo
    0969
    Germany
    29
    ST, T1-T2, DF
    LL00-LL01-LL02-LL03, A
    [CF, CIF, S, CI, C]
    [B, BI, K, L, CI, C]
    D, DI, P, S
    D, LL3-LL2-LL1-LL0
    4
    Grapholox
    10000
    France
    26
    LL01-LL02-LL03, DF
    LL00, L, T1, A
    [CF, CIF, K, CI, C]
    [B, T2, SRT, S, C]
    D, LL3-LL2-LL1
    D, P, DI, LL0
    5
    Thornton
    AA010
    England
    27
    LL01-LL02-LL03, DF
    K, A, R1-R2
    [CF, CI, ISd,ITd,Td,Sd, C]
    [T2-T1, ST, S, C]
    D, LL3-LL2-LL1
    D, L LL00, LL0
    6
    Diwa/Deeva
    720
    Denmark
    /India 25
    LL00, L, K, A
    LL01-LL02-LL03, DF
    [B, S, ST, T, C]
    [CF, CIF, CI, C]
    D, DI, P, LL0
    D, LL3-LL2-LL1
    7
    Shanghai
    F.F.1003
    China
    34
    SH0-SH1, CU1-CU2-CU3
    LL03-LL02-LL01-LL00, DF
    [L, T0-T1-T2, S, SRT, C]
    [CF, CIF, H0-H1, P, CI,C]
    D, SQ2-SQ1, TH0, CH1
    D, LL0-LL1-LL2-LL3
    8
    Hemmi
    P262
    Japan
    25
    LL01-LL02-LL03, DF
    K, A, R1-R2
    [CF, CIF, CI, C]
    [T2-T1, ST, S, C]
    D, LL3-LL2-LL1
    D, L LL00, LL0
    9
    Pickett
    N3-ES
    USA
    32
    R1-R2, K, A
    LL0/LL00, LL1/LL01, DF
    [B, ST, S, T1-T2, CI, C]
    [CF, CIF, Ln, L, CI, C]
    D, DI, K1-K2-K3
    D, LL2/LL02, LL3/LL03
    10
    K & E
    68 1100
    USA
    26
    Sq1-Sq2, DF
    Ln-3,Ln-2,Ln-1,Ln-0, A
    [CF, CIF, L, CI, C]
    [B, T, SRT, S, C]
    D, Ln0-Ln1-Ln2-Ln3
    D, DI, K
    11
    Dietgen
    1741
    USA
    24
    K, T1, T2, DF
    LL03-LL02-LL01, W2
    [CF, CIF, CI, C]
    [ W2', L, C, W1']
    D, S, ST, P
    W1, LL1-LL2-LL3
    (12) Beacon   313
    Korea
    24
    (want to collect)   L, K, A
    LL/1-LL/2-LL/3, DF
    [ B, T, S, ST, C]
    [CF, CIF, CI, C]
    D, DI, LL0, LL/0
    D, LL3-LL2-LL1


  • Circular   type

    #
    maker
    model
    country
    rules
            front   rear diameter
    1
    Gilson
    Atlas (Type 3)
    USA
    16
    C, S-Log, 25 Spiral C,
    C-Log, Coils, Constants
    (Deg, Sin, Tan) * 3,
    Fractions-Decimal
    21cm, 8.25"
    2
    Dietzgen/Gilson
    Binary 1797B
    USA
    21
    C, CI, A, K, L, LL(4 rev),
    Fractions, drill/thread, mm
    (Deg, Sin, Tan) * 3,
    Fractions-Decimal
    21cm, 8.25"
    3
    S.I.C.
    1610-D
    Japan
    26
    LL3-LL2-LL1-LL0, K, A, D
    [C, CI, B, EI]
    , P, L, DI, D
    [C, T, S, T, S, T, ST]
    13cm, 5"
      * Atlas and Binary have double cursors and 1610-D has a single cursor with a circular slide on either side.


    Ref.:   % Calculation Comparison

    source 10+20%= 10-20%= 10x20%= 10/20%=
    30+10+20%
    =
    abaee.com 12 8 2
    "% not work
    this case"
    48

    Microsoft 12 8 20 5
    48

    Calculator.net 10.2 9.8 2 50
    40.2

    Naver.com 10.2 9.8 2 50
    40.2

    useful 12 8 2 Many different ideas
    48

      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