Theoretical DistributionsPYQ Jan 26Question 4595 of 230
All Questions

If the first quartile (Q1\displaystyle Q_1) and third quartile (Q3\displaystyle Q_3) of a normal distribution are 22 and 28, what is the median of the distribution?

Options

A22
B25
C30
D28
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b25

All Options:

  • A22
  • B25
  • C30
  • D28

Detailed Solution & Explanation

A normal distribution is perfectly symmetric about its center. Because of this symmetry, the mean, median, and mode of a normal distribution are all equal and lie exactly at the midpoint of the distribution. Consequently, the first quartile (Q1\displaystyle Q_1) and the third quartile (Q3\displaystyle Q_3) are equidistant from the median: Median=Q1+Q32\text{Median} = \frac{Q_1 + Q_3}{2}
We are given: - Q1=22\displaystyle Q_1 = 22 - Q3=28\displaystyle Q_3 = 28
Substituting these values into the formula: Median=22+282=502=25\text{Median} = \frac{22 + 28}{2} = \frac{50}{2} = 25 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.

More Questions from Theoretical Distributions

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free