Theoretical DistributionsMCQMTP May 19 Series IIQuestion 3569 of 230
All Questions

The mean deviation about median of a standard normal variate is

Options

A0.675σ\displaystyle 0.675 \sigma
B0.675\displaystyle 0.675
C0.80σ\displaystyle 0.80 \sigma
D0.80\displaystyle 0.80
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Correct Answer

✅ Option d — 0.80\displaystyle 0.80

All Options:

  • A0.675σ\displaystyle 0.675 \sigma
  • B0.675\displaystyle 0.675
  • C0.80σ\displaystyle 0.80 \sigma
  • D0.80\displaystyle 0.80

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Detailed Solution & Explanation

**Mean Deviation of a Standard Normal Variate** Let Z\displaystyle Z be a standard normal variate. **First Principles:** 1. By definition, a standard normal distribution has: - Mean μ=0\displaystyle \mu = 0 - Standard deviation σ=1\displaystyle \sigma = 1 2. Since the standard normal curve is symmetrical about the mean, the mean and median are equal: Median=Mean=0\text{Median} = \text{Mean} = 0 3. The Mean Deviation (MD) about the median is equivalent to the Mean Deviation about the mean: MD=E[∣Z−Median∣]=E[∣Z∣]MD = E[|Z - \text{Median}|] = E[|Z|] 4. For any normal distribution, the Mean Deviation is: MD=σ2π≈0.7979σ≈0.80σMD = \sigma \sqrt{\frac{2}{\pi}} \approx 0.7979\sigma \approx 0.80\sigma 5. For a standard normal variate where σ=1\displaystyle \sigma = 1: MD≈0.80×1=0.80MD \approx 0.80 \times 1 = 0.80 Thus, the mean deviation about median is 0.80\displaystyle 0.80, which corresponds to Option D (or Option C, since 0.80σ=0.80\displaystyle 0.80\sigma = 0.80 when σ=1\displaystyle \sigma=1). *Note:* The textbook key lists Option A (0.675σ\displaystyle 0.675\sigma), which is actually the formula for the Quartile Deviation (QD) of a normal distribution, not the Mean Deviation. 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

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

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For a Poisson distribution,

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