Central Tendency & DispersionMTP Oct 21Question 2903 of 473
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The algebraic sum of the deviations of a frequency distribution from its mean is always,

Options

Agreater than zero
Bless than zero
Czero
DNone of these
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Correct Answer

✅ Option c — zero

All Options:

  • Agreater than zero
  • Bless than zero
  • Czero
  • DNone of these

Detailed Solution & Explanation

**Step 1: State the fundamental property.** For any set of observations x1,x2,…,xn\displaystyle x_1, x_2, \ldots, x_n with mean xˉ\displaystyle \bar{x}: ∑fi(xi−xˉ)=∑fixi−xˉ∑fi=Nxˉ−xˉ⋅N=0\sum f_i(x_i - \bar{x}) = \sum f_i x_i - \bar{x} \sum f_i = N\bar{x} - \bar{x} \cdot N = 0 where xˉ=∑fixi∑fi=∑fixiN\displaystyle \bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{\sum f_i x_i}{N}. **Step 2: Conclusion.** The algebraic sum of deviations of a frequency distribution from its mean is always **zero**. Hence, **Option C** is the correct answer.

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