Theoretical DistributionsMCQPYQ June 24Question 3556 of 230
All Questions

For a normal distribution, the ratio of mean deviation to the standard deviation is _____

Options

A0.4
B0.6
C0.8
D1.0
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Correct Answer

✅ Option c — 0.8

All Options:

  • A0.4
  • B0.6
  • C0.8
  • D1.0

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Detailed Solution & Explanation

**Ratio of Mean Deviation to Standard Deviation in Normal Distribution** For a normal distribution with standard deviation σ\displaystyle \sigma, the mean deviation (MD) about its mean is given by: MD=2πσ≈0.7979σMD = \sqrt{\frac{2}{\pi}} \sigma \approx 0.7979 \sigma In fractional approximation commonly used in textbooks: MD≈45σ=0.8σMD \approx \frac{4}{5} \sigma = 0.8 \sigma We need to find the ratio of the mean deviation to the standard deviation: Ratio=MDσ\text{Ratio} = \frac{MD}{\sigma} Using the standard approximation: MDσ≈0.8σσ=0.8\frac{MD}{\sigma} \approx \frac{0.8 \sigma}{\sigma} = 0.8 Hence, **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.

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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