sum (xi - x) is equal to

Option d: Zero. Solution: Step 1: Expand the sum. sumi=1n(xi - x) = sumi=1n xi - sumi=1n x = sum xi - nx Step 2: Substitute the definition of x . Since x = xin , we have nx = sum xi . sum(xi - x) = 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.

Measures of Central Tendency and DispersionMCQPYQ 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

For any discrepancies in this question, email contact@cadada.in

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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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