The mean deviation from an average A will be minimum, if A represents:

This question was previously asked in
SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. Median.
  2. Harmonic mean.
  3. Mode.
  4. Arithmetic mean.

Answer (Detailed Solution Below)

Option 1 : Median.
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Detailed Solution

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Explanation

Mean deviation from an average = MDX

⇒ MDX = 1/N(∑xi – A), A is average

⇒ Mean deviation from the median = MDmed

⇒ MDmed = 1/n(xi – Md)

Mean deviation about an arbituary point is minimum when the point is median

Coefficient of mean deviation = MDX/x̅, where x̅ is arithmetic meran

Coefficient of mean deviation based on MDmed/Md

∴ MDmed/Md = Minimum(MDx/x̅ 

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