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Properties of Measures of Central Tendency

If the standa...

Question

If the standard deviation of $2 x_{i} + 3$ is 8, then the variance of $\frac{3 x_{i}}{2} .$

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Solution

$S D (2 x_{i}) + 3 = 8$
SD of $(2 x_{i}) = 8$ [SD does not alter when term is decreased by fixed constant]
SD of $x_{i} = 4$
$V a r (x_{i}) = S D^{2} = 16$
$V a r (\frac{3 x_{i}}{2} = (\frac{9}{4}) V a r (x_{i})$
$= (\frac{9}{4}) 16 = 36$

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Properties of Measures of Central Tendency

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