The sum of absolute deviations is minimized by: MCQ with Answer and Explanation

The sum of absolute deviations is minimized by:
A. Geometric mean
B. Mode
C. Mean
D. Median
Answer: Option D
Solution (By JKExamLibrary)
Median minimizes Σ |x - M|.

This question belongs to: Accountancy and Statistics Statistics

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Practice More Statistics Questions

Question #1 Report Error
For a normal distribution, the relationship between Quartile Deviation (QD), Mean Deviation (MD), and Standard Deviation (SD) is roughly:
A. SD = MD = QD
B. 6 SD = 5 MD = 4 QD
C. 4 SD = 5 MD = 6 QD
D. 2 SD = 3 MD = 4 QD

Correct Answer: Option C


Explanation:
In a perfectly normal distribution, QD is about 2/3 of SD, and MD is about 4/5 of SD, yielding the 4:5:6 ratio.

This question belongs to: Accountancy and Statistics Statistics
Question #2 Report Error
A cumulative frequency distribution shows the number of observations:
A. Less than or more than certain values
B. Exactly equal to a value
C. Only in the first class
D. In the modal class

Correct Answer: Option A


Explanation:
Cumulative frequencies sum frequencies up to a certain point (less than type) or from a point (more than type).

This question belongs to: Accountancy and Statistics Statistics
Question #3 Report Error
Data on attributes is said to be consistent if:
A. All class frequencies are positive integers
B. No calculated class frequency is negative, as negative frequencies are impossible
C. Attributes are independent of each other
D. The sum of all frequencies equals the sample size

Correct Answer: Option B


Explanation:
Consistency requires that all derived class frequencies (including ultimate classes) are non-negative, as negative counts are logically impossible in real-world data.

This question belongs to: Accountancy and Statistics Statistics