Measures of Central Tendency and DispersionPYQ Jan 26Question 4584 of 473
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If arithmetic mean of two numbers is 64 and harmonic mean is 16 then geometric mean is

Options

A64
B16
C32
D8
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Correct Answer

✅ Option c — 32

All Options:

  • A64
  • B16
  • C32
  • D8

Detailed Solution & Explanation

The relationship between the Arithmetic Mean (AM\displaystyle AM), Geometric Mean (GM\displaystyle GM), and Harmonic Mean (HM\displaystyle HM) for any set of positive numbers is given by the formula: GM2=AM×HMGM^2 = AM \times HM
We are given: - AM=64\displaystyle AM = 64 - HM=16\displaystyle HM = 16
Substituting these values into the formula: GM2=64×16GM^2 = 64 \times 16 GM=64×16GM = \sqrt{64 \times 16}
Using the properties of square roots: GM=64×16GM = \sqrt{64} \times \sqrt{16} GM=8×4=32GM = 8 \times 4 = 32 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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