Which measure of central tendency is defined only when all observations are positive? MCQ with Answer and Explanation

Which measure of central tendency is defined only when all observations are positive?
A. Median
B. Arithmetic mean
C. Mode
D. Geometric mean (for meaningful result) and Harmonic mean (for positive numbers, but GM is undefined for negatives/zero)
Answer: Option D
Solution (By JKSSB Mock Tests)
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.

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Practice More Statistics Questions

Question #1
The geometric mean of a set of values is less than or equal to the arithmetic mean. This is known as:
A. Time reversal test
B. Central limit theorem
C. AM-GM inequality
D. Bayes' theorem

Correct Answer: Option C


Explanation:
For non-negative numbers, AM ≥ GM always holds.

This question belongs to: Accountancy and Statistics Statistics
Question #2
A good questionnaire should have:
A. Many open-ended questions to confuse
B. Double negatives for clarity
C. Simple and clear language
D. Questions arranged in random order

Correct Answer: Option C


Explanation:
Clarity and simplicity are fundamental principles.

This question belongs to: Accountancy and Statistics Statistics
Question #3
A set of values has mean 20. If each value is multiplied by 2 and then 5 is added, the new mean is:
A. 40
B. 25
C. 50
D. 45

Correct Answer: Option D


Explanation:
New mean = 2 × 20 + 5 = 45.

This question belongs to: Accountancy and Statistics Statistics