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

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

Central Tendency & DispersionPYQ 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.

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