Central Tendency & DispersionPYQ Nov 18Question 2857 of 473

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

\displaystyle >0

\displaystyle =0

\displaystyle <0

DNone of these

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Correct Answer

✅ Option b — $\displaystyle =0$

**Step 1: Define algebraic sum of deviations.** Let

\displaystyle x_1, x_2, \ldots, x_n

be observations with arithmetic mean

\displaystyle \bar{x}

. Algebraic sum of deviations

\displaystyle = \sum_{i=1}^{n}(x_i - \bar{x})

**Step 2: Expand the sum.**

\sum_{i=1}^{n}(x_i - \bar{x}) = \sum_{i=1}^{n} x_i - n\bar{x}

**Step 3: Substitute

\displaystyle \bar{x} = \frac{\sum x_i}{n}

.**

= \sum x_i - n \cdot \frac{\sum x_i}{n} = \sum x_i - \sum x_i = 0

**Conclusion:** The algebraic sum of deviations from the arithmetic mean is always **zero**. Hence, **Option B** is the correct answer.

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