Assertion (A): Fisher's index is called 'ideal' because it satisfies important mathematical tests. Reason (R): It is the geometric mean of Laspeyres and Paasche indices, balancing their biases. MCQ with Answer and Explanation

Assertion (A): Fisher's index is called 'ideal' because it satisfies important mathematical tests. Reason (R): It is the geometric mean of Laspeyres and Paasche indices, balancing their biases.
A. Both A and R are true, and R is the correct explanation of A
B. Both A and R are true, but R is not the correct explanation of A
C. A is true but R is false
D. A is false but R is true
Answer: Option A
Solution (By JKExamLibrary)
Fisher's index earns the 'ideal' designation by satisfying time reversal and factor reversal tests, achieved through its geometric mean formulation that mitigates the upward bias of Laspeyres and downward bias of Paasche.

This question belongs to: Accountancy and Statistics Statistics

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Question #1 Report Error
In a Poisson distribution, the probability of zero successes is e^{-λ}. If λ=3, this probability is approximately:
A. 0.10
B. 0.15
C. 0.05
D. 0.20

Correct Answer: Option C


Explanation:
e^{-3} ≈ 0.0498 ≈ 0.05.

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Question #2 Report Error
In a distribution with extreme outliers, which measure of central tendency is most appropriate?
A. Harmonic mean
B. Median
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Correct Answer: Option B


Explanation:
The median is resistant to outliers and gives a better central value for skewed distributions.

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Which measure of central tendency is defined only when all observations are positive?
A. Median
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D. Geometric mean (for meaningful result) and Harmonic mean (for positive numbers, but GM is undefined for negatives/zero)

Correct Answer: Option D


Explanation:
Geometric mean requires all positive values; otherwise it's undefined or zero. Harmonic mean also requires non-zero values, but GM is more restricted. Actually, GM is defined only for positive data if we want real numbers. So C.

This question belongs to: Accountancy and Statistics Statistics