Theoretical DistributionsMCQPYQ June 22Question 3551 of 230
All Questions

In a normal distribution, variance is 16 then the value of mean deviation is.

Options

A4.2
B3.2
C4.5
D2.5
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Correct Answer

✅ Option b — 3.2

All Options:

  • A4.2
  • B3.2
  • C4.5
  • D2.5

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Detailed Solution & Explanation

**Mean Deviation of a Normal Distribution** For a normal distribution with standard deviation σ\displaystyle \sigma, the relationship between standard deviation and mean deviation (MD) is given by: MD≈0.7979σMD \approx 0.7979 \sigma Alternatively, in fractional approximation: MD=45σ=0.8σMD = \frac{4}{5} \sigma = 0.8 \sigma **Given:** - Variance (σ2\displaystyle \sigma^2) =16  ⟹  σ=16=4\displaystyle = 16 \implies \sigma = \sqrt{16} = 4 **Step 1: Calculate the Mean Deviation** MD=0.8×4=3.2MD = 0.8 \times 4 = 3.2 Using the more precise decimal formula: MD≈0.7979×4=3.1916≈3.2MD \approx 0.7979 \times 4 = 3.1916 \approx 3.2 Hence, **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.

Key Concepts to Understand

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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