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A set of n values x1, x2,..., xn has standard deviation σ. What is the standard deviation of n values x1 + k, x2 + k,..., xn + k ? 
1. σ 
2. σ + k
3. σ - k
4. kσ 

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Correct Answer - Option 1 : σ 

Concept:

if each observation is increased by a constant k, then the standard deviation is unchanged.

Calculations:

Given, A set of n values x1, x2,..., xn has standard deviation σ.

Consider, the data x1 + k, x2 + k,..., xn + k

Here, each observation is increased by a constant k,

we know that, if each observation is increased by a constant k, then the standard deviation is unchanged.

Hence, the standard deviation of n values x1 + k, x2 + k,..., xn + k is σ

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