Theoretical DistributionsMCQMTP Dec 22 - Series IIQuestion 3591 of 230
All Questions

For a normal distribution, the first and third quartile are given to be 37 and 49, the mode of the distribution is.

Options

A37
B49
C43
D45
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Correct Answer

✅ Option c — 43

All Options:

  • A37
  • B49
  • C43
  • D45

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Detailed Solution & Explanation

**Mode of Normal Distribution from Quartiles** We are given: - First quartile Q1=37\displaystyle Q_1 = 37 - Third quartile Q3=49\displaystyle Q_3 = 49 **First Principles:** 1. By definition, a normal distribution is perfectly symmetric about its center. 2. In a symmetric distribution, the median lies exactly at the midpoint of the first and third quartiles: Median=Q1+Q32\text{Median} = \frac{Q_1 + Q_3}{2} 3. For any normal distribution, the mean, median, and mode are all equal: Mode=Median=Mean\text{Mode} = \text{Median} = \text{Mean} **Step 1: Calculate the median** Median=37+492=862=43\text{Median} = \frac{37 + 49}{2} = \frac{86}{2} = 43 **Step 2: Determine the mode** Mode=Median=43\text{Mode} = \text{Median} = 43 This matches 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.

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