The Geometric mean of 3, 6, 24 and 48 is

Option b: 12. Solution: Step 1: Recall the formula for Geometric Mean. GM = (x1 × x2 × x3 × x4)1/n where n is the number of observations. Step 2: Calculate the product. 3 × 6 × 24 × 48 = 3 × 6 = 18 18 × 24 = 432 432 × 48 = 20736 Step 3: Take the 4th root. GM = (20736)1/4 20736 = 124? Check: 122 = 144 , 124 = 1442 = 20736 ✓ So GM = 12 . The correct answer is 12 , which is Option B. Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Nov. 18Question 2997 of 473

All Questions

The Geometric mean of $\displaystyle 3, 6, 24$ and $\displaystyle 48$ is

Options

\displaystyle 8

\displaystyle 12

\displaystyle 24

\displaystyle 6

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Correct Answer

✅ Option b — $\displaystyle 12$

All Options:

A $\displaystyle 8$
B $\displaystyle 12$
C $\displaystyle 24$
D $\displaystyle 6$

Detailed Solution & Explanation

**Step 1: Recall the formula for Geometric Mean.**

\text{GM} = (x_1 \times x_2 \times x_3 \times x_4)^{1/n}

where

\displaystyle n

is the number of observations. **Step 2: Calculate the product.**

3 \times 6 \times 24 \times 48

= 3 \times 6 = 18

18 \times 24 = 432

432 \times 48 = 20736

**Step 3: Take the 4th root.**

\text{GM} = (20736)^{1/4}

20736 = 12^4?

Check:

\displaystyle 12^2 = 144

\displaystyle 12^4 = 144^2 = 20736

✓ So

\displaystyle \text{GM} = 12

. The correct answer is

\displaystyle 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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The Geometric mean of 3,6,24\displaystyle 3, 6, 243,6,24 and 48\displaystyle 4848 is