Mathematics · Statistics
Given below are two statements: Assertion (A): For a given set of observations X and constants a and b, SD(X + a) = SD(X – b) = SD(X) and SD(aX) = |a| · SD(X). Reason (R): Standard deviation is independent of change of origin, but not independent of change of scale. In light of the above statements, choose the most appropriate answer:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(A) is true, but (R) is false
- 2(A) is false, but (R) is true
- 3Both (A) and (R) are true, but (R) is NOT the correct explanation of (A)
- 4Both (A) and (R) are true, and (R) is the correct explanation of (A)✓
Correct answer
Both (A) and (R) are true, and (R) is the correct explanation of (A)
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