InterviewSolution
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InterviewSolution
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The standard deviation of variate `x_i` is σ. Then standard deviation of the variate `(ax_i+b)/c` where `a, b, c ` are constants is- (a) `(a/c)sigma` (b) `|a/c| sigma` (c) (a^2/c^2)sigma` (d) Non of theseA. `((a)/(c ))sigma`B. `|(a)/(c )|sigma`C. `((a^(2))/(c^(2)))sigma`D. None of these |
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Answer» Correct Answer - B Let `y=(alpha x+b)/(c ), i.e., y=(a)/(c )x+(b)/(c )` i.e., `y=(a)/(c )x+(b)/(c )` `therefore overline (y)=Aoverline(x)+B` `therefore y-overline(y)=A(x-overline(x))` `implies (y-overline(y))^(2)=A^(2)(x-overline(x))^(2)` `implies sum (y-overline(y))^(2)=A^(2)sum(x-overline(x))^(2)` `implies n. sigma_(y)^(2)=A^(2). n sigma_(x)^(2)` `implies sigma_(y)^(2)=A^(2)sigma_(x)^(2)` `implies sigma_(y)=|A|sigma_(x)` `implies sigma_(y)=|(a)/(c )| sigma_(x)` Thus, new SD `=|(a)/(c )|sigma` |
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