Central Tendency & DispersionPYQ Nov. 19Question 2953 of 473
All Questions

The deviations are minimum taken from:

Options

AMean
BMedian
CMode
DNone of these
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Correct Answer

✅ Option b — Median

All Options:

  • AMean
  • BMedian
  • CMode
  • DNone of these

Detailed Solution & Explanation

A fundamental property of the median is that the sum of the absolute deviations of a set of observations from any value is minimized when that value is the median. Mathematically, for a set of values x1,x2,…,xn\displaystyle x_1, x_2, \dots, x_n: ∑i=1n∣xi−A∣ is minimized when A=Median\sum_{i=1}^n |x_i - A| \text{ is minimized when } A = \text{Median} In contrast, the sum of the squared deviations is minimized when taken from the arithmetic mean. Therefore, the deviations (meaning absolute deviations) are minimum when taken from the median. Hence, **Option B** is the correct answer.

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