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Properties of Measures of Central Tendency

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Question

What will be the value of mean and standard deviation if each value is decreased by $5$ and then multiplied by $5$ ?

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Solution

$\frac{\sum x_{1}}{n} = 70$
$\Rightarrow \sum x_{1} = 5 (3500 + 50 \times 5)$
$= 5 \times 3750 = 18750$
New mean $= \frac{\sum x_{1}}{n} = \frac{18750}{50} = 375$
New S.D $= 5 \times 8 = 40.$
Hence, the answer is $375, 40.$

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