GATE 2011 CS (CS1) – Question 43
A finite sequence X has mean μₓ and standard deviation σₓ. Define yᵢ=axᵢ+b for positive constants a,b. Which is incorrect?
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Correct answer: (D) σᵧ=aσₓ+b
Explanation
Positive scaling preserves order and equal-value frequencies, so median and mode positions are preserved. Mean transforms affinely. Standard deviation depends on differences from the mean, so translation b cancels and σᵧ=aσₓ. Adding b to standard deviation is incorrect, D.