Discussion
Suppose \(\sigma_{1}\) = standard deviation of {1, 2, 3, 4, 5}
\(\sigma_{2}\) = standard deviation of {11, 12, 13, 14, 15}
then ...............
Answer: C
The two standard deviations are equal: \(\sigma_{1} = \sigma_{2}\).
The second set is the first set with 10 added to every value. Adding a constant shifts the mean by the same constant, so every deviation from the mean is unchanged, and so is the standard deviation. Both sets have deviations \(-2, -1, 0, 1, 2\), giving
\[ \sigma = \sqrt{\frac{4+1+0+1+4}{5}} = \sqrt{2} \]
Option D confuses the standard deviation with the mean, which does rise by 10.
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