Theoretical DistributionsMCQMTP May 19Question 3566 of 230
All Questions

If the mean deviation of a normal variable is 16, what is its quartile deviation?

Options

A10.00
B13.50
C15.00
D12.05
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Correct Answer

✅ Option b — 13.50

All Options:

  • A10.00
  • B13.50
  • C15.00
  • D12.05

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Detailed Solution & Explanation

**Quartile Deviation from Mean Deviation** Let X\displaystyle X be a normal variable with standard deviation σ\displaystyle \sigma. **Step 1: Relations between parameters in Normal Distribution** For a normal distribution, the Mean Deviation (MD) and Quartile Deviation (QD) are related to the standard deviation (S.D. or σ\displaystyle \sigma) by the following approximations: Mean Deviation (MD)≈0.8σ\text{Mean Deviation (MD)} \approx 0.8\sigma Quartile Deviation (QD)≈0.675σ\text{Quartile Deviation (QD)} \approx 0.675\sigma **Step 2: Find standard deviation σ\displaystyle \sigma** Given that MD=16\displaystyle MD = 16: 16=0.8σ16 = 0.8\sigma σ=160.8=20\sigma = \frac{16}{0.8} = 20 **Step 3: Calculate the Quartile Deviation (QD)** Substitute σ=20\displaystyle \sigma = 20 into the Quartile Deviation formula: QD=0.675×20=13.50QD = 0.675 \times 20 = 13.50 This matches Option B. Hence, **Option B** 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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