Central Tendency & DispersionMTP Dec 2023 Series IQuestion 2923 of 473
All Questions

The algebraic sum of the deviations of set of values from their arithmetic mean is

Options

A>0\displaystyle >0
B<0\displaystyle <0
C0\displaystyle 0
DNone of these
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Correct Answer

✅ Option c — 0\displaystyle 0

All Options:

  • A>0\displaystyle >0
  • B<0\displaystyle <0
  • C0\displaystyle 0
  • DNone of these

Detailed Solution & Explanation

**Step 1: Apply the fundamental theorem.** For observations x1,x2,…,xn\displaystyle x_1, x_2, \ldots, x_n with AM xˉ\displaystyle \bar{x}: ∑i=1n(xi−xˉ)=∑xi−nxˉ=nxˉ−nxˉ=0\sum_{i=1}^{n}(x_i - \bar{x}) = \sum x_i - n\bar{x} = n\bar{x} - n\bar{x} = 0 **Conclusion:** The algebraic sum is always **zero** (Option C). **Note:** The `correct_option` given as A (>0\displaystyle > 0) is incorrect. The correct answer is C (0\displaystyle 0). Hence, **Option C** is the correct answer.

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