For a normal distribution Q1 = 54.32 and Q3 = 78.86 , then the median of the distribution is

Option c: 66.59. Solution: Median of a Normal Distribution For a normal distribution, the probability density curve is perfectly symmetrical about its mean . Because of this symmetry, the median lies exactly at the midpoint of the first quartile ( Q1 ) and the third quartile ( Q3 ). Thus, we can write: = 1 + Q3/2 Given values: - First Quartile ( Q1 ) = 54.32 - Third Quartile ( Q3 ) = 78.86 Calculation: = 54.32 + 78.86/2 = 133.18/2 = 66.59 Thus, the median of the distribution is 66.59 , which corresponds to Option C. Hence, Option C is the correct answer.

For a normal distribution $Q_1 = 54.32$ and $Q_3 = 78.86$, then the median of the distribution is

The correct answer is Option c: 66.59. **Median of a Normal Distribution** For a normal distribution, the probability density curve is perfectly symmetrical about its mean $\\mu$. Because of this symmetry, the median lies exactly at the midpoint of the first quartile ($Q_1$) and the third quartile ($Q_3$). Thus, we can write: $$\\text{Median} = \\frac{Q_1 + Q_3}{2}$$ **Given values:** - First Quartile ($Q_1$) = $54.32$ - Third Quartile ($Q_3$) = $78.86$ **Calculation:** $$\\text{Median} = \\frac{54.32 + 78.86}{2} = \\frac{133.18}{2} = 66.59$$ Thus, the median of the distribution is $66.59$, which corresponds to Option C. Hence, **Option C** is the correct answer.

Theoretical DistributionsMCQMTP Nov 21Question 3583 of 230

All Questions

For a normal distribution $\displaystyle Q_1 = 54.32$ and $\displaystyle Q_3 = 78.86$ , then the median of the distribution is

Options

A12.17

B39.43

C66.59

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 66.59

All Options:

A12.17
B39.43
C66.59
DNone of these

Detailed Solution & Explanation

**Median of a Normal Distribution** For a normal distribution, the probability density curve is perfectly symmetrical about its mean

\displaystyle \\mu

. Because of this symmetry, the median lies exactly at the midpoint of the first quartile (

\displaystyle Q_1

) and the third quartile (

\displaystyle Q_3

). Thus, we can write:

\\text{Median} = \\frac{Q_1 + Q_3}{2}

**Given values:** - First Quartile (

\displaystyle Q_1

) =

\displaystyle 54.32

- Third Quartile (

\displaystyle Q_3

) =

\displaystyle 78.86

**Calculation:**

\\text{Median} = \\frac{54.32 + 78.86}{2} = \\frac{133.18}{2} = 66.59

Thus, the median of the distribution is

\displaystyle 66.59

, 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

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.

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

For a normal distribution Q1=54.32\displaystyle Q_1 = 54.32Q1​=54.32 and Q3=78.86\displaystyle Q_3 = 78.86Q3​=78.86, then the median of the distribution is