Measures of Central Tendency and DispersionMCQPYQ Nov. 18Question 2997 of 473
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The Geometric mean of $3, 6, 24\displaystyle and $48 is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $12$

All Options:

  • A8\displaystyle 8
  • B$12$
  • C$24$
  • D6\displaystyle 6

Detailed Solution & Explanation

**Step 1: Recall the formula for Geometric Mean.** GM=(x1×x2×x3×x4)1/nGM\displaystyle \text{GM} = (x_1 ×\displaystyle \times x_2 ×\displaystyle \times x_3 ×\displaystyle \times x_4)^{1/n} where n\displaystyle n is the number of observations. **Step 2: Calculate the product.** 3×6×24×483 ×\displaystyle \times 6 ×\displaystyle \times 24 ×\displaystyle \times 48 =3×6=18= 3 ×\displaystyle \times 6 = 18 18×24=43218 ×\displaystyle \times 24 = 432 432×48=20736432 ×\displaystyle \times 48 = 20736 **Step 3: Take the 4th root.** GM=(20736)1/4GM\displaystyle \text{GM} = (20736)^{1/4} 20736=124?20736 = 12^4? Check: $12^2 = 144\displaystyle , $12^4 = 144^2 = 20736 ✓ So GM=12\displaystyle GM=12\displaystyle \text{GM} = 12. The correct answer is $12$, which is **Option B**. 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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