Theoretical DistributionsMCQPYQ July 21Question 3548 of 230
All Questions

In normal distribution, Mean, Median and Mode are:

Options

AZero
BNot Equal
CEqual
DNull
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Correct Answer

✅ Option c — Equal

All Options:

  • AZero
  • BNot Equal
  • CEqual
  • DNull

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Detailed Solution & Explanation

**Measures of Central Tendency in a Normal Distribution** A normal distribution has the following characteristic properties: 1. **Symmetry**: The probability density curve is perfectly symmetric about its center, meaning 50%\displaystyle 50\% of the observations lie to the left of the center and 50%\displaystyle 50\% to the right. Therefore, the Median is at the center. 2. **Unimodality**: The curve has a single peak at the center where the probability density is highest. Thus, the Mode is also at the center. 3. **Mean**: The center of the distribution corresponds to the mean μ\displaystyle \mu. Because of these geometric properties of the symmetric, bell-shaped normal curve, the three central measures coincide at the center: Mean=Median=Mode\text{Mean} = \text{Median} = \text{Mode} 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

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.

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.

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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