Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 2953 of 473
All Questions

The deviations are minimum taken from:

Options

AMean
BMedian
CMode
DNone of these
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Correct Answer

✅ Option b — Median

All Options:

  • AMean
  • BMedian
  • CMode
  • DNone of these

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Detailed Solution & Explanation

A fundamental property of the median is that the sum of the absolute deviations of a set of observations from any value is minimized when that value is the median. Mathematically, for a set of values x1,x2,…,xn\displaystyle x_1, x_2, \dots, x_n: ∑i=1n∣xi−A∣ is minimized when A=Median\sum_{i=1}^n |x_i - A| \text{ is minimized when } A = \text{Median} In contrast, the sum of the squared deviations is minimized when taken from the arithmetic mean. Therefore, the deviations (meaning absolute deviations) are minimum when taken from the median. Hence, **Option B** 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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