Theoretical DistributionsMCQMTP Dec 2023 Series IQuestion 3600 of 230
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If the two Quartiles N(μ,σ2)\displaystyle N(\mu, \sigma^2) are 14.6\displaystyle 14.6 and 25.4\displaystyle 25.4 respectively. What is the standard deviation of the distribution?

Options

A9\displaystyle 9
B6\displaystyle 6
C10\displaystyle 10
D8\displaystyle 8
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Correct Answer

✅ Option d — 8\displaystyle 8

All Options:

  • A9\displaystyle 9
  • B6\displaystyle 6
  • C10\displaystyle 10
  • D8\displaystyle 8

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Detailed Solution & Explanation

**Finding Standard Deviation from Quartiles** We are given the two quartiles of a normal distribution N(mu,sigma2)\displaystyle N(\\mu, \\sigma^2): - First Quartile (Q1\displaystyle Q_1) = 14.6\displaystyle 14.6 - Third Quartile (Q3\displaystyle Q_3) = 25.4\displaystyle 25.4 **Step 1: Calculate the Quartile Deviation (QD)** The Quartile Deviation is defined as: textQD=fracQ3−Q12\\text{QD} = \\frac{Q_3 - Q_1}{2} Substituting the given values: textQD=frac25.4−14.62=frac10.82=5.4\\text{QD} = \\frac{25.4 - 14.6}{2} = \\frac{10.8}{2} = 5.4 **Step 2: Relate QD to Standard Deviation (sigma\displaystyle \\sigma)** For any normal distribution, the relation is: textQDapprox0.6745sigma\\text{QD} \\approx 0.6745\\sigma Substituting textQD=5.4\displaystyle \\text{QD} = 5.4: 0.6745sigma=5.40.6745\\sigma = 5.4 sigma=frac5.40.6745approx8.006approx8\\sigma = \\frac{5.4}{0.6745} \\approx 8.006 \\approx 8 Thus, the standard deviation is 8\displaystyle 8, which corresponds to Option D. Hence, **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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