Central Tendency & DispersionMTP June 24 Series IQuestion 3024 of 473
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The rate of returns from three different shares are 100%,200%\displaystyle 100\%, 200\% and 400%\displaystyle 400\% respectively. The average rate of return will be.

Options

A350%\displaystyle 350\%
B233.33%\displaystyle 233.33\%
C200%\displaystyle 200\%
D300%\displaystyle 300\%
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Correct Answer

✅ Option c — 200%\displaystyle 200\%

All Options:

  • A350%\displaystyle 350\%
  • B233.33%\displaystyle 233.33\%
  • C200%\displaystyle 200\%
  • D300%\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.** - 100%=2\displaystyle 100\% = 2 (original + 100% return) - 200%=3\displaystyle 200\% = 3 - 400%=5\displaystyle 400\% = 5 Actually for rates of return, we use the percentage values directly: x1=100,x2=200,x3=400\displaystyle x_1 = 100, x_2 = 200, x_3 = 400 **Step 3: Calculate GM.** GM=(100×200×400)1/3=(8,000,000)1/3\text{GM} = (100 \times 200 \times 400)^{1/3} = (8{,}000{,}000)^{1/3} =(8×106)1/3=2×102=200%= (8 \times 10^6)^{1/3} = 2 \times 10^2 = 200\% **Verification:** 100×200×400=8,000,000=(200)3\displaystyle 100 \times 200 \times 400 = 8{,}000{,}000 = (200)^3 ✓ Hence, **Option C** is the correct answer.

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