Which property of the arithmetic mean states that the sum of deviations from the mean is always zero?
A. Invariance under change of origin
B. Sum of deviations property
C. Linearity
D. Minimum sum of squared deviations
Answer: Option B
Solution (By JKSSB Mock Tests)
The sum of deviations of all observations from their arithmetic mean is always zero, i.e., Σ(x - x̄) = 0, which is a fundamental algebraic property of the mean.
Explanation:
Only Fisher's Ideal Index satisfies both the Time Reversal and Factor Reversal Tests; Laspeyres and Marshall-Edgeworth fail the factor test.
Explanation:
Direct standardization uses the study population's age-specific death rates applied to the standard population's age structure; thus, only the study population's age-specific rates are needed.
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