Central Tendency & DispersionMTP May 19 Series IIQuestion 2882 of 473
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If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is

Options

A0
B5
C-5
DNone of these
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Correct Answer

✅ Option a — 0

All Options:

  • A0
  • B5
  • C-5
  • DNone of these

Detailed Solution & Explanation

**Step 1: Compute AM.** xˉ=15+20+253=603=20\bar{x} = \frac{15 + 20 + 25}{3} = \frac{60}{3} = 20 **Step 2: Calculate deviations.** | xi\displaystyle x_i | xi−xˉ\displaystyle x_i - \bar{x} | |--------|------------------| | 15 | −5\displaystyle -5 | | 20 | 0\displaystyle 0 | | 25 | 5\displaystyle 5 | **Step 3: Sum of deviations.** ∑(xi−xˉ)=−5+0+5=0\sum(x_i - \bar{x}) = -5 + 0 + 5 = 0 This is a fundamental property of arithmetic mean. Hence, **Option A** is the correct answer.

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