The rate of returns 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. For averaging rates of return (proportional/ratio data), the Geometric Mean is the appropriate measure. Step 2: Convert to multipliers. - 100% = 2 (original + 100% return) - 200% = 3 - 400% = 5 Actually for rates of return, we use the percentage values directly: x1 = 100, x2 = 200, x3 = 400 Step 3: Calculate GM. GM = (100 × 200 × 400)1/3 = (8,000,000)1/3 = (8 × 106)1/3 = 2 × 102 = 200% Verification: 100 × 200 × 400 = 8,000,000 = (200)3 ✓ Hence, Option C is the correct answer.

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

The correct answer is Option c: $200\%$. **Step 1: Identify the appropriate average for rates of return.** For averaging rates of return (proportional/ratio data), the **Geometric Mean** is the appropriate measure. **Step 2: Convert to multipliers.** - $100\% = 2$ (original + 100% return) - $200\% = 3$ - $400\% = 5$ Actually for rates of return, we use the percentage values directly: $x_1 = 100, x_2 = 200, x_3 = 400$ **Step 3: Calculate GM.** $$\text{GM} = (100 \times 200 \times 400)^{1/3} = (8{,}000{,}000)^{1/3}$$ $$= (8 \times 10^6)^{1/3} = 2 \times 10^2 = 200\%$$ **Verification:** $100 \times 200 \times 400 = 8{,}000{,}000 = (200)^3$ ✓ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 3024 of 473

All Questions

The rate of returns from three different shares are $\displaystyle 100\%, 200\%$ 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.** For averaging rates of return (proportional/ratio data), the **Geometric Mean** is the appropriate measure. **Step 2: Convert to multipliers.** -

\displaystyle 100\% = 2

(original + 100% return) -

\displaystyle 200\% = 3

\displaystyle 400\% = 5

Actually for rates of return, we use the percentage values directly:

\displaystyle x_1 = 100, x_2 = 200, x_3 = 400

**Step 3: Calculate GM.**

\text{GM} = (100 \times 200 \times 400)^{1/3} = (8{,}000{,}000)^{1/3}

= (8 \times 10^6)^{1/3} = 2 \times 10^2 = 200\%

**Verification:**

\displaystyle 100 \times 200 \times 400 = 8{,}000{,}000 = (200)^3

✓ 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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The rate of returns from three different shares are 100%,200%\displaystyle 100\%, 200\%100%,200% and 400%\displaystyle 400\%400% respectively. The average rate of return will be.