The algebraic sum of deviations of observations from the arithmetic mean is: MCQ with Answer and Explanation

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The algebraic sum of deviations of observations from the arithmetic mean is:

A. Always zero

B. Always positive

C. Always negative

D. Minimum

Answer: Option A

Solution (By JKSSB Mock Tests)

Σ(x - x̄) = 0 is a fundamental property of the arithmetic mean.

This question belongs to: Accountancy and Statistics Statistics

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Question #1

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For a set of discrete values, which measure of central tendency minimizes the sum of squared deviations?

A. Median

B. Arithmetic Mean

C. Mode

D. Harmonic Mean

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Correct Answer: Option B

Explanation:
A fundamental property of the arithmetic mean is that the sum of the squares of deviations from it is always minimum.

This question belongs to: Accountancy and Statistics Statistics

Question #2

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If a dataset has a mean of 100 and a coefficient of variation of 20%, the standard deviation is:

A. 20

B. 10

C. 40

D. 30

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Correct Answer: Option A

Explanation:
Coefficient of variation (CV) = (SD / Mean) × 100. So 20 = (SD / 100) × 100 → SD = 20. CV standardizes dispersion relative to the mean.

This question belongs to: Accountancy and Statistics Statistics

Question #3

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If Σp₁q₀ = 720 and Σp₀q₀ = 600, the Laspeyres price index is:

A. 120

B. 1200

C. 83.33

D. 60

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Correct Answer: Option A

Explanation:
P_L = 720/600 × 100 = 120.

This question belongs to: Accountancy and Statistics Statistics

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