Measures of Central Tendency and DispersionMCQPYQ Dec 22Question 2958 of 473
All Questions

Mean deviation is minimum when deviations are taken from:

Options

AMean
BMedian
CMode
DHarmonic Mean
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Correct Answer

✅ Option b — Median

All Options:

  • AMean
  • BMedian
  • CMode
  • DHarmonic Mean

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Detailed Solution & Explanation

The mean deviation (M.D.) of a set of observations is the arithmetic mean of the absolute values of the deviations of the observations from some average (Mean, Median, or Mode). A mathematical property of mean deviation is that the mean deviation is minimum when the deviations are taken from the **Median**. Mathematically, for a set of values xi\displaystyle x_i: 1n∑i=1n∣xi−A∣ is minimum when A=Median\frac{1}{n} \sum_{i=1}^n |x_i - A| \text{ is minimum when } A = \text{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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