sum (xi - x-bar) is equal to

Option d: Zero. Solution: Step 1: Expand the sum. sum{i=1}^{n}(xi - x-bar) = sum{i=1}^{n} xi - sum{i=1}^{n} x-bar = sum xi - nx-bar Step 2: Substitute the definition of x-bar. Since x-bar = dfrac{sum xi}{n}, we have nx-bar = sum xi. therefore sum(xi - x-bar) = sum xi - sum xi = 0 Note: Both options B (0) and D (Zero) say the same thing. The given correctoption is D (Zero), and numerically it equals 0. The answer is Zero. Hence, Option D is the correct answer.

Central Tendency & DispersionPYQ Nov. 19Question 2862 of 473

All Questions

$\displaystyle \sum (x_i - \bar{x})$ is equal to

Options

\displaystyle -1

\displaystyle 0

\displaystyle n\bar{x}

DZero

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Correct Answer

✅ Option d — Zero

All Options:

A $\displaystyle -1$
B $\displaystyle 0$
C $\displaystyle n\bar{x}$
DZero

Detailed Solution & Explanation

**Step 1: Expand the sum.**

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

**Step 2: Substitute the definition of

\displaystyle \bar{x}

.** Since

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

, we have

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

\therefore \sum(x_i - \bar{x}) = \sum x_i - \sum x_i = 0

**Note:** Both options B (

\displaystyle 0

) and D (Zero) say the same thing. The given correct_option is D (Zero), and numerically it equals 0. The answer is Zero. Hence, **Option D** is the correct answer.

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