Measures of Central Tendency and DispersionMCQMTP Nov 18Question 3050 of 473
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Relationship between AM, GM, and HM

Options

AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
BAM≥GM≤HM\displaystyle AM \geq GM \leq HM
CHM≥AM≥GM\displaystyle HM \geq AM \geq GM
Dnone of these
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Correct Answer

✅ Option a — AM≥GM≥HM\displaystyle AM \geq GM \geq HM

All Options:

  • AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
  • BAM≥GM≤HM\displaystyle AM \geq GM \leq HM
  • CHM≥AM≥GM\displaystyle HM \geq AM \geq GM
  • Dnone of these

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Detailed Solution & Explanation

**Step 1: Recall the standard inequality between AM, GM, and HM.** For any set of positive real numbers, the following inequality always holds: AM≥GM≥HM\text{AM} \geq \text{GM} \geq \text{HM} with equality if and only if all values are equal. **Step 2: Evaluate the options.** - Option A: AM≥GM≥HM\displaystyle AM \geq GM \geq HM — this is the **correct** mathematical inequality. - Option C: HM≥AM≥GM\displaystyle HM \geq AM \geq GM — this is incorrect (reverses the inequality). **Conclusion:** The correct relationship is AM ≥ GM ≥ HM, which is **Option A**. Note: The exam key says C, but that's mathematically wrong. The correct answer is A. 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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