If the rates return from three different shares are 100% , 200% and 400% respectively. The average rate of return will be.

Option c: 200%. Solution: Step 1: Identify the appropriate average. For rates of return, the Geometric Mean is theoretically appropriate. However, for simple average of rates, the AM may be used. Step 2: Calculate AM. AM = 100 + 200 + 400/3 = 700/3 = 233.33% Step 3: Calculate GM. GM = (100 × 200 × 400)1/3 = (8 × 106)1/3 = 200% Step 4: From exam key (A = 350%). 350% doesn't correspond to AM, GM, or HM in any standard computation here. For rate of return (multiplicative growth), GM = 200% is correct (Option C). For simple average, AM = 233.33% (Option B). Hence, Option C is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 21Question 3059 of 473

All Questions

If the rates return from three different shares are $\displaystyle 100\%$ , $\displaystyle 200\%$ and $\displaystyle 400\%$ respectively. The average rate of return will be.

Options

\displaystyle 350\%

\displaystyle 233.33\%

\displaystyle 200\%

\displaystyle 300\%

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Correct Answer

✅ Option c — $\displaystyle 200\%$

All Options:

A $\displaystyle 350\%$
B $\displaystyle 233.33\%$
C $\displaystyle 200\%$
D $\displaystyle 300\%$

Detailed Solution & Explanation

**Step 1: Identify the appropriate average.** For rates of return, the Geometric Mean is theoretically appropriate. However, for simple average of rates, the AM may be used. **Step 2: Calculate AM.**

\text{AM} = \frac{100 + 200 + 400}{3} = \frac{700}{3} = 233.33\%

**Step 3: Calculate GM.**

\text{GM} = (100 \times 200 \times 400)^{1/3} = (8 \times 10^6)^{1/3} = 200\%

**Step 4: From exam key (A = 350%).**

\displaystyle 350\%

doesn't correspond to AM, GM, or HM in any standard computation here. For rate of return (multiplicative growth), **GM = 200%** is correct (Option C). For simple average, **AM = 233.33%** (Option B). Hence, **Option C** 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 the rates return from three different shares are 100%\displaystyle 100\%100%, 200%\displaystyle 200\%200% and 400%\displaystyle 400\%400% respectively. The average rate of return will be.