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The standard deviation of $3x+7$ is $4$; then what is the variance of $x$? I know that variance is the square of the standard deviation but how does $3x+7$ and $x$ relate?

swapedoc
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2 Answers2

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Hints: Adding a constant doesn't change the standard deviation. What does multiplying by a constant do?

Robert Israel
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  • multiplying by constant makes sd=constant * sd. If that is so :- Then 3x=4 or SD of x= 4/3 then variance =16/9?? – swapedoc Dec 13 '13 at 13:38
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If the standard deviation of $3x+7$ is $4$, then the standard deviation of $x$ is $4/3$. So the variance must be $16/9$.

When you multiply data by a constant, you multiply the standard deviation by that same constant. You can prove this to yourself by using the formula defining standard deviation. Left as an exercise for the student, of course.

William Chang
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richard1941
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    What if the constant is negative? When the standard deviation gets multiplied by the constant, does it become negative too? – Dilip Sarwate Mar 08 '14 at 03:25