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

Option b: 13.50. Solution: Finding Quartile Deviation from Mean Deviation any normal distribution, we have the following standard decimal approximations:1. Mean Deviation (MD): ≈ 0.8 2. Quartile Deviation (QD): ≈ 0.675 Given:- Mean Deviation of the normal variable is = 16 .Step 1: Calculate the Standard Deviation ( ) the relation = 0.8 : 16 = 0.8 = 16/0.8 = 20 Step 2: Calculate the Quartile Deviation (QD) the relation = 0.675 : = 0.675 × 20 = 13.50 Alternative Method (Direct Ratio): = 0.675/0.80 × = 27/32 × = 16 : = 27/32 × 16 = 27/2 = 13.50 Checking the options:- Option A: 10 ✗- Option B: 13.50 ✓- Option C: 15 ✗- Option D: 12.50 ✗, Option B is the correct answer.

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

The correct answer is Option b: 13.50. **Finding Quartile Deviation from Mean Deviation**\n\nFor any normal distribution, we have the following standard decimal approximations:\n1. **Mean Deviation (MD):** $\\text{MD} \\approx 0.8\\sigma$\n2. **Quartile Deviation (QD):** $\\text{QD} \\approx 0.675\\sigma$\n\n**Given:**\n- Mean Deviation of the normal variable is $\\text{MD} = 16$.\n\n**Step 1: Calculate the Standard Deviation ($\\sigma$)**\nUsing the relation $\\text{MD} = 0.8\\sigma$:\n$$16 = 0.8\\sigma$$\n$$\\sigma = \\frac{16}{0.8} = 20$$\n\n**Step 2: Calculate the Quartile Deviation (QD)**\nUsing the relation $\\text{QD} = 0.675\\sigma$:\n$$\\text{QD} = 0.675 \\times 20 = 13.50$$\n\n**Alternative Method (Direct Ratio):**\n$$\\text{QD} = \\frac{0.675}{0.80} \\times \\text{MD} = \\frac{27}{32} \\times \\text{MD}$$\nSubstituting $\\text{MD} = 16$:\n$$\\text{QD} = \\frac{27}{32} \\times 16 = \\frac{27}{2} = 13.50$$\n\n**Checking the options:**\n- Option A: $10$ ✗\n- **Option B: $13.50$** ✓\n- Option C: $15$ ✗\n- Option D: $12.50$ ✗\n\nHence, **Option B** is the correct answer.

Theoretical DistributionsMCQMTP June 24 Series IIQuestion 3606 of 230

All Questions

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

Options

A10

B13.50

C15

D12.50

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 13.50

All Options:

A10
B13.50
C15
D12.50

Detailed Solution & Explanation

**Finding Quartile Deviation from Mean Deviation**\n\nFor any normal distribution, we have the following standard decimal approximations:\n1. **Mean Deviation (MD):**

\displaystyle \\text{MD} \\approx 0.8\\sigma

\n2. **Quartile Deviation (QD):**

\displaystyle \\text{QD} \\approx 0.675\\sigma

\n\n**Given:**\n- Mean Deviation of the normal variable is

\displaystyle \\text{MD} = 16

.\n\n**Step 1: Calculate the Standard Deviation (

\displaystyle \\sigma

)**\nUsing the relation

\displaystyle \\text{MD} = 0.8\\sigma

:\n

16 = 0.8\\sigma

\\sigma = \\frac{16}{0.8} = 20

\n\n**Step 2: Calculate the Quartile Deviation (QD)**\nUsing the relation

\displaystyle \\text{QD} = 0.675\\sigma

:\n

\\text{QD} = 0.675 \\times 20 = 13.50

\n\n**Alternative Method (Direct Ratio):**\n

\\text{QD} = \\frac{0.675}{0.80} \\times \\text{MD} = \\frac{27}{32} \\times \\text{MD}

\nSubstituting

\displaystyle \\text{MD} = 16

:\n

\\text{QD} = \\frac{27}{32} \\times 16 = \\frac{27}{2} = 13.50

\n\n**Checking the options:**\n- Option A:

\displaystyle 10

✗\n- **Option B:

\displaystyle 13.50

** ✓\n- Option C:

\displaystyle 15

✗\n- Option D:

\displaystyle 12.50

✗\n\nHence, **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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If the mean deviation of a normal variable is 16\displaystyle 1616, what is its quartile deviation?