Measures of Central Tendency and DispersionMCQPYQ Dec 21Question 3031 of 473
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If the AM and GM for 10 observations are both 15, then the value of HM is

Options

ALess than 15
BMore than 15
C15
DCannot be determined
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Correct Answer

✅ Option c — 15

All Options:

  • ALess than 15
  • BMore than 15
  • C15
  • DCannot be determined

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Detailed Solution & Explanation

**Step 1: Recall the relationship AM × HM = GM².** GM2=AM×HM\text{GM}^2 = \text{AM} \times \text{HM} **Step 2: Substitute given values.** - AM = 15, GM = 15 152=15×HM15^2 = 15 \times \text{HM} 225=15×HM225 = 15 \times \text{HM} HM=15\text{HM} = 15 **Step 3: Verify using the inequality AM ≥ GM ≥ HM.** Equality holds when all observations are equal. Since AM = GM = 15, all 10 observations must be equal to 15, which means HM = 15 as well. **Conclusion:** HM = 15. Hence, **Option C** 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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