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A set of $\mathrm{n}$ values $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ has standard deviation $\sigma$. What will be the standard deviation of $n$ values $\mathrm{x}_1+\mathrm{k}, \mathrm{x}_2+\mathrm{k}, \ldots, \mathrm{x}_{\mathrm{n}}+\mathrm{k} ?$
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If each observation is increased by a constant $\mathrm{k}$, then standard deviation is unchanged. So, $\sigma$ will be the standard deviation.
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