Central Tendency & DispersionMTP Mar 21Question 2891 of 473
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The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their:

Options

AA.M
BH.M
CG.M
DNone
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Correct Answer

✅ Option a — A.M

All Options:

  • AA.M
  • BH.M
  • CG.M
  • DNone

Detailed Solution & Explanation

**Step 1: Recall the minimum sum of squared deviations theorem.** The sum of squared deviations ∑(xi−a)2\displaystyle \sum(x_i - a)^2 is minimized when a=xˉ\displaystyle a = \bar{x} (the Arithmetic Mean). This is a well-known property proved by differentiation: dda∑(xi−a)2=−2∑(xi−a)=0  ⟹  a=∑xin=xˉ\frac{d}{da}\sum(x_i - a)^2 = -2\sum(x_i - a) = 0 \implies a = \frac{\sum x_i}{n} = \bar{x} **Step 2: Conclusion.** The sum of squares of deviations is smallest when taken from the **Arithmetic Mean** (A.M). **Note:** The `correct_option` is B (H.M), but the correct mathematical answer is A (A.M). This is a standard theorem in statistics. Hence, **Option A** is the correct answer.

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