Consider three observations a, b and c such that b = a + c. If the standard deviation of: Statistics

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Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

(1) b2 = 3(a2 + c2) + 9d2

(2) b2 = a2 + c2 + 3d2

(3) b2 = 3(a2 + c2 + d2)

(4) b2 = 3(a2 + c2) – 9d2

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Why doesn't variance is not affected by adding any constant value with same amount

rudranshsingh