Scaling is done in the optional subjects of the mains exam for every student in every paper. It is primarily done to nullify the (dis)advantage of one optional over another. Although UPSC might be doing some complex statistical analysis, but generally the following formula gives approximately the same result.
Scaled marks = M + (x - m) S/s
where
M = Overall mean of raw marks (unscaled marks) of every student of every optional
m = Mean of raw marks (unscaled marks) of every student of your optional
x = Your raw marks (unscaled marks) in your optional
S = Standard Deviation of raw marks (unscaled marks) of every student of every optional
s = Standard Deviation of raw marks (unscaled marks) of every student of your optional
Scaled marks = M + (x - m) S/s
where
M = Overall mean of raw marks (unscaled marks) of every student of every optional
m = Mean of raw marks (unscaled marks) of every student of your optional
x = Your raw marks (unscaled marks) in your optional
S = Standard Deviation of raw marks (unscaled marks) of every student of every optional
s = Standard Deviation of raw marks (unscaled marks) of every student of your optional
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