Measures of Central Tendency and DispersionMCQPYQ Dec. 21Question 2865 of 473
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If there are 3 observations 15, 20, 25 then sum of deviation of the observations from AM is

Options

A0\displaystyle 0
B5\displaystyle 5
C−5\displaystyle -5
D10\displaystyle 10
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Correct Answer

✅ Option a — 0\displaystyle 0

All Options:

  • A0\displaystyle 0
  • B5\displaystyle 5
  • C−5\displaystyle -5
  • D10\displaystyle 10

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Detailed Solution & Explanation

**Step 1: Compute the arithmetic mean.** xˉ=15+20+253=603=20\bar{x} = \frac{15 + 20 + 25}{3} = \frac{60}{3} = 20 **Step 2: Compute deviations from AM.** | xi\displaystyle x_i | xi−xˉ\displaystyle x_i - \bar{x} | |--------|------------------| | 15 | 15−20=−5\displaystyle 15 - 20 = -5 | | 20 | 20−20=0\displaystyle 20 - 20 = 0 | | 25 | 25−20=5\displaystyle 25 - 20 = 5 | **Step 3: Sum of deviations.** ∑(xi−xˉ)=−5+0+5=0\sum(x_i - \bar{x}) = -5 + 0 + 5 = 0 This confirms the fundamental property: the algebraic sum of deviations from AM is always zero. Hence, **Option A** 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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