Central Tendency & DispersionMTP June 22Question 3108 of 473
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The sum of squares of the deviations of the given values from their ................. is minimum.

Options

AArithmetic Mean
BMedian
CMode
DGM
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Correct Answer

✅ Option a — Arithmetic Mean

All Options:

  • AArithmetic Mean
  • BMedian
  • CMode
  • DGM

Detailed Solution & Explanation

A fundamental property of the arithmetic mean is that the sum of the squared deviations of a set of observations from their arithmetic mean is less than the sum of the squared deviations from any other value. Mathematically, for a set of values x1,x2,…,xn\displaystyle x_1, x_2, \dots, x_n: ∑i=1n(xi−A)2 is minimized when A=Arithmetic Mean\sum_{i=1}^n (x_i - A)^2 \text{ is minimized when } A = \text{Arithmetic Mean} Hence, **Option A** is the correct answer.

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