Theoretical DistributionsMCQMTP Dec 2023 Series IIQuestion 3603 of 230
All Questions

An approximate relation between quartile deviation (QD) and standard deviation (S.D.) of normal distribution is:

Options

A5QD=4SD\displaystyle 5QD = 4 SD
B4QD=5SD\displaystyle 4 QD = 5 SD
C2QD=SD\displaystyle 2 QD = SD
D3QD=2SD\displaystyle 3 QD = 2 SD
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Correct Answer

✅ Option d — 3QD=2SD\displaystyle 3 QD = 2 SD

All Options:

  • A5QD=4SD\displaystyle 5QD = 4 SD
  • B4QD=5SD\displaystyle 4 QD = 5 SD
  • C2QD=SD\displaystyle 2 QD = SD
  • D3QD=2SD\displaystyle 3 QD = 2 SD

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Detailed Solution & Explanation

**Relationship Between Quartile Deviation and Standard Deviation**\n\nFor a normal distribution, the three main measures of dispersion are:\n1. **Standard Deviation (SD):** sigma\displaystyle \\sigma\n2. **Mean Deviation (MD):** textMDapprox0.8sigma=frac45textSD\displaystyle \\text{MD} \\approx 0.8\\sigma = \\frac{4}{5}\\text{SD}\n3. **Quartile Deviation (QD):** textQDapprox0.675sigmaapproxfrac23textSD\displaystyle \\text{QD} \\approx 0.675\\sigma \\approx \\frac{2}{3}\\text{SD}\n\n**Approximate Ratio of Dispersion Measures:**\nThe relationship between QD, MD, and SD can be expressed as:\ntextQD:textMD:textSDapprox10:12:15\\text{QD} : \\text{MD} : \\text{SD} \\approx 10 : 12 : 15\n\nFrom this ratio, we can establish the relations between individual measures:\n- Between QD and SD:\n fractextQDtextSDapproxfrac1015=frac23\\frac{\\text{QD}}{\\text{SD}} \\approx \\frac{10}{15} = \\frac{2}{3}\n textQDapproxfrac23textSD\\text{QD} \\approx \\frac{2}{3} \\text{SD}\n 3textQDapprox2textSD3\\text{QD} \\approx 2\\text{SD}\n\n**Checking the options:**\n- Option A: 5textQD=4textSD\displaystyle 5\\text{QD} = 4\\text{SD} ✗\n- Option B: 4textQD=5textSD\displaystyle 4\\text{QD} = 5\\text{SD} ✗\n- Option C: 2textQD=textSD\displaystyle 2\\text{QD} = \\text{SD} ✗\n- **Option D: 3textQD=2textSD\displaystyle 3\\text{QD} = 2\\text{SD}** ✓\n\nHence, **Option D** 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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