If two variables a and b are related by c = ab then GM. of c =

Option b: GM of a × GM of b. Solution: Step 1: Recall the fundamental property of Geometric Mean. For n paired observations where ci = ai × bi : GM(c) = (producti=1n ci)1/n = (producti=1n ai bi)1/n = (producti=1n ai)1/n × (producti=1n bi)1/n = GM(a) × GM(b) Step 2: Conclusion. If c = ab , then GM(c) = GM(a) × GM(b) . This matches Option B (GM of a × GM of b ). Note: The given correct option is D, but mathematically when c = a × b , GM (c) = GM (a) × GM (b) , which is Option B. (If c = a/b , then GM (c) = GM (a) /GM (b) = Option D.) Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Mar 22Question 3007 of 473

All Questions

If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then GM. of $\displaystyle c$ =

Options

AGM of

\displaystyle a

+ GM of

\displaystyle b

BGM of

\displaystyle a \times

GM of

\displaystyle b

CGM of

\displaystyle a

- GM of

\displaystyle b

DGM of

\displaystyle a

/ GM of

\displaystyle b

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Correct Answer

✅ Option b — GM of $\displaystyle a \times$ GM of $\displaystyle b$

All Options:

AGM of $\displaystyle a$ + GM of $\displaystyle b$
BGM of $\displaystyle a \times$ GM of $\displaystyle b$
CGM of $\displaystyle a$ - GM of $\displaystyle b$
DGM of $\displaystyle a$ / GM of $\displaystyle b$

Detailed Solution & Explanation

**Step 1: Recall the fundamental property of Geometric Mean.** For

\displaystyle n

paired observations where

\displaystyle c_i = a_i \cdot b_i

\text{GM}(c) = \left(\prod_{i=1}^{n} c_i\right)^{1/n} = \left(\prod_{i=1}^{n} a_i b_i\right)^{1/n}

= \left(\prod_{i=1}^{n} a_i\right)^{1/n} \times \left(\prod_{i=1}^{n} b_i\right)^{1/n} = \text{GM}(a) \times \text{GM}(b)

**Step 2: Conclusion.** If

\displaystyle c = ab

, then

\displaystyle \text{GM}(c) = \text{GM}(a) \times \text{GM}(b)

. This matches **Option B** (GM of

\displaystyle a

× GM of

\displaystyle b

). Note: The given correct option is D, but mathematically when

\displaystyle c = a \times b

, GM

\displaystyle (c)

= GM

\displaystyle (a)

× GM

\displaystyle (b)

, which is **Option B**. (If

\displaystyle c = a/b

, then GM

\displaystyle (c)

= GM

\displaystyle (a)

/GM

\displaystyle (b)

= Option D.) 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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If two variables a\displaystyle aa and b\displaystyle bb are related by c=ab\displaystyle c = abc=ab then GM. of c\displaystyle cc =