Theoretical DistributionsMTP Dec 2023 Series IQuestion 3995 of 230
All Questions

If the Quartile Deviation of a normal distribution with mean 10\displaystyle 10 and SD 4\displaystyle 4 is

Options

A0.675\displaystyle 0.675
B67.50\displaystyle 67.50
C2.70\displaystyle 2.70
D3.20\displaystyle 3.20
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Correct Answer

✅ Option c — 2.70\displaystyle 2.70

All Options:

  • A0.675\displaystyle 0.675
  • B67.50\displaystyle 67.50
  • C2.70\displaystyle 2.70
  • D3.20\displaystyle 3.20

Detailed Solution & Explanation

**Quartile Deviation of a Normal Distribution**\n\nFor any normal distribution, the relationship between the Quartiles and the Standard Deviation (sigma\displaystyle \\sigma) is defined as follows:\n- The first quartile (Q1\displaystyle Q_1) is located at approximately mu−0.675sigma\displaystyle \\mu - 0.675\\sigma.\n- The third quartile (Q3\displaystyle Q_3) is located at approximately mu+0.675sigma\displaystyle \\mu + 0.675\\sigma.\n\nThe **Quartile Deviation (QD)** is defined as:\ntextQD=fracQ3−Q12\\text{QD} = \\frac{Q_3 - Q_1}{2}\n\nSubstituting the expressions for Q1\displaystyle Q_1 and Q3\displaystyle Q_3:\ntextQD=frac(mu+0.675sigma)−(mu−0.675sigma)2\\text{QD} = \\frac{(\\mu + 0.675\\sigma) - (\\mu - 0.675\\sigma)}{2}\ntextQD=frac2times0.675sigma2=0.675sigma\\text{QD} = \\frac{2 \\times 0.675\\sigma}{2} = 0.675\\sigma\n\n**Given:**\n- Mean mu=10\displaystyle \\mu = 10\n- Standard deviation sigma=4\displaystyle \\sigma = 4\n\n**Calculating the Quartile Deviation:**\ntextQD=0.675timessigma\\text{QD} = 0.675 \\times \\sigma\ntextQD=0.675times4=2.70\\text{QD} = 0.675 \\times 4 = 2.70\n\n**Checking the options:**\n- Option A: 0.675\displaystyle 0.675 (this is the ratio textQD/sigma\displaystyle \\text{QD}/\\sigma) ✗\n- Option B: 67.50\displaystyle 67.50 ✗\n- **Option C: 2.70\displaystyle 2.70** ✓\n- Option D: 3.20\displaystyle 3.20 ✗\n\nTherefore, the Quartile Deviation is 2.70\displaystyle 2.70.\n\nHence, **Option C** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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