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A set of $n$ values $x_{1}, x_{2}, \ldots, x_{n}$ has standard deviation $\sigma$. What is the standard deviation of $n$ values $x_{1}+k_{1} x_{2}+k_{1, \ldots,} x_{n}+k ?$
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We know that, if a number is added in values, then the standard deviation remains unaltered.
$\therefore$ Standard deviation of new values $=\sigma$
$\therefore$ Standard deviation of new values $=\sigma$
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