Population-Weighted Exams Ranking

This is a well-thought-out scientifically modeled, postulated and argued ranking method.
Both the Percentage average marks and the number of students in an exam center are involved or considered.
Let the number of students per exam center also called population be M and the percentage average marks be M. Performance index is designated as P.

P = M*(1 + 0.1*LogN)
where LogN is the logarithm to Base 10 of N

Example
Einstein Academy had 95% with 25 students while Pumbavu School had 23% with 120 students. Calculate Performance index P.

Solution; P for Einstein Academy = 95*(1+0.1*Log25) = 108.28
Performance P for Pumbavu School = 23*(1+0.1*Log120) = 27.78

The ‘weighting’ factor is a function of N. The higher the value of N, the higher the P.

Selected values for emphasis and clarity.
M100 with N1 gives P=100
M100 with N20 gives P=113.01
M100 with N450 gives P=126.53

M87 with N50 gives P=101.78

M90 with N1 is equivalent to M86.94 with N50
M90 with N20 is equivalent to M82.68 with N200
M90 with N450 is equivalent to M80.38 with N450

This formula works best with Percentage average marks and not Total marks. It can also be used to compare individual subjects in any exam.


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Population-Weighted Performance Exams
Ranking
_______________________________
The formula converts a school's average %
marks and the number of students who sat the
exam therein, to a linear parameter called Performance index (P) which can be used for
ranking.
While deriving this formula, I was inspired by
other Logarithmic scales e.g. Decibel :-used in
sound power and Richter scale:- used to
quantify earthquake intensity. _____________________________
This is a well-thought-out scientifically
modeled, postulated and argued ranking
method.
Both the Percentage average marks and the
number of students in an exam center are involved or considered.
___________________________
Let the number of students per exam center
also called population be N and the
percentage average marks be M. Performance
index is designated as P.
Performance= M*(1 + 0.1*LogN)
where LogN is the
logarithm to Base 10 of N
_____________
Example
Einstein Academy had M=95% with N=25
students while Pumbavu School had M=23%
with N=120 students. Calculate Performance index P.
Solution; P for Einstein Academy = 95*
(1+0.1*Log25) = 108.28
Performance P for Pumbavu School = 23*
(1+0.1*Log120) = 27.78
_________________________
The ‘weighting’ factor is a function of N. The
higher the value of N, the higher the
weighting factor.
If the percentage average marks(M) is held
constant, a higher N value yields a higher
performance P. _________________________
Selected values for emphasis and clarity.
M100 with N1 gives P=100
M100 with N20 gives P=113.01
M100 with N450 gives P=126.53
M87 with N50 gives P=101.78 M90 with N1 is equivalent to M86.94 with N50
M90 with N20 is equivalent to M82.68 with
N200
M90 with N450 is equivalent to M80.38 with
N450
_______________________________ The formula works best with Percentage
Average Marks and not Total Marks.
_________________________
@creativekaggs intellectual property.