If standard deviation of a Poisson distribution is 2 , then its Mode

Option c: 3 and 4. Solution: Mode of a Poisson Distribution given Standard Deviation Given: - Standard Deviation ( .D. ) = 2 Step 1: Find the parameter m (mean/variance) of the Poisson distribution The standard deviation of a Poisson distribution is given by (m) . (m) = 2 m = 22 = 4 Since the parameter m is a positive integer ( m = 4 ), the Poisson distribution is bi-modal. Step 2: Determine the modes of the distribution For a Poisson distribution, if the parameter m is an integer, the two modes are: 1 = m - 1 = 4 - 1 = 3 2 = m = 4 Thus, the modes of the distribution are 3 and 4 , which corresponds to Option C. Hence, Option C is the correct answer.

If standard deviation of a Poisson distribution is $2$, then its Mode

The correct answer is Option c: $3$ and $4$. **Mode of a Poisson Distribution given Standard Deviation** **Given:** - Standard Deviation ($\\text{S.D.}$) = $2$ **Step 1: Find the parameter $m$ (mean/variance) of the Poisson distribution** The standard deviation of a Poisson distribution is given by $\\sqrt{m}$. $$\\sqrt{m} = 2 \\implies m = 2^2 = 4$$ Since the parameter $m$ is a positive integer ($m = 4$), the Poisson distribution is bi-modal. **Step 2: Determine the modes of the distribution** For a Poisson distribution, if the parameter $m$ is an integer, the two modes are: $$\\text{Mode}_1 = m - 1 = 4 - 1 = 3$$ $$\\text{Mode}_2 = m = 4$$ Thus, the modes of the distribution are $3$ and $4$, which corresponds to Option C. Hence, **Option C** is the correct answer.

Theoretical DistributionsMCQMTP June 24 Series IQuestion 3533 of 230

All Questions

If standard deviation of a Poisson distribution is $\displaystyle 2$ , then its Mode

Options

\displaystyle 2

\displaystyle 4

\displaystyle 3

and

\displaystyle 4

\displaystyle 3

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Correct Answer

✅ Option c — $\displaystyle 3$ and $\displaystyle 4$

All Options:

A $\displaystyle 2$
B $\displaystyle 4$
C $\displaystyle 3$ and $\displaystyle 4$
D $\displaystyle 3$

Detailed Solution & Explanation

**Mode of a Poisson Distribution given Standard Deviation** **Given:** - Standard Deviation (

\displaystyle \\text{S.D.}

) =

\displaystyle 2

**Step 1: Find the parameter

\displaystyle m

(mean/variance) of the Poisson distribution** The standard deviation of a Poisson distribution is given by

\displaystyle \\sqrt{m}

\\sqrt{m} = 2 \\implies m = 2^2 = 4

Since the parameter

\displaystyle m

is a positive integer (

\displaystyle m = 4

), the Poisson distribution is bi-modal. **Step 2: Determine the modes of the distribution** For a Poisson distribution, if the parameter

\displaystyle m

is an integer, the two modes are:

\\text{Mode}_1 = m - 1 = 4 - 1 = 3

\\text{Mode}_2 = m = 4

Thus, the modes of the distribution are

\displaystyle 3

and

\displaystyle 4

, which corresponds to Option C. 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

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

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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If standard deviation of a Poisson distribution is 2\displaystyle 22, then its Mode