Geometric Mean of 3, 7, 11, 15, 24, 28, 30, 0 is

Option b: 0. Solution: Step 1: Recall the formula for Geometric Mean. GM = (x1 × x2 × x3 × ×s × xn)1/n Step 2: Identify any zero values. The data set includes 0 as one of the observations: 3, 7, 11, 15, 24, 28, 30, 0 . Step 3: Compute the product. 3 × 7 × 11 × 15 × 24 × 28 × 30 × 0 = 0 (Any product containing 0 equals 0 .) Step 4: Compute GM. GM = (0)1/8 = 0 Since the data set contains a zero, the Geometric Mean is 0 . Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ June 24Question 3005 of 473

All Questions

Geometric Mean of $\displaystyle 3, 7, 11, 15, 24, 28, 30, 0$ is

Options

D12

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Correct Answer

✅ Option b — 0

All Options:

Detailed Solution & Explanation

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

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

**Step 2: Identify any zero values.** The data set includes

\displaystyle 0

as one of the observations:

\displaystyle \{3, 7, 11, 15, 24, 28, 30, 0\}

. **Step 3: Compute the product.**

3 \times 7 \times 11 \times 15 \times 24 \times 28 \times 30 \times 0 = 0

(Any product containing

\displaystyle 0

equals

\displaystyle 0

.) **Step 4: Compute GM.**

\text{GM} = (0)^{1/8} = 0

Since the data set contains a zero, the Geometric Mean is

\displaystyle \mathbf{0}

. 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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Geometric Mean of 3,7,11,15,24,28,30,0\displaystyle 3, 7, 11, 15, 24, 28, 30, 03,7,11,15,24,28,30,0 is