The quartiles of a variable are 45 , 52 and 75 respectively. Its quartile deviation is

Option a: 15. Solution: We are given the quartiles of a variable: - First quartile ( Q1 ) = 45 - Second quartile (Median, Q2 ) = 52 - Third quartile ( Q3 ) = 75 The quartile deviation (Q.D.) is calculated as: Q.D. = Q3 - Q1/2 = 75 - 45/2 = 30/2 = 15 Hence, Option A is the correct answer.

The quartiles of a variable are $45$, $52$ and $75$ respectively. Its quartile deviation is

The correct answer is Option a: $15$. We are given the quartiles of a variable: - First quartile ($Q_1$) = $45$ - Second quartile (Median, $Q_2$) = $52$ - Third quartile ($Q_3$) = $75$ The quartile deviation (Q.D.) is calculated as: $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{75 - 45}{2} = \frac{30}{2} = 15$$ Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP May 20Question 3238 of 473

All Questions

The quartiles of a variable are $\displaystyle 45$ , $\displaystyle 52$ and $\displaystyle 75$ respectively. Its quartile deviation is

Options

\displaystyle 15

\displaystyle 20

\displaystyle 25

\displaystyle 8.30

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

Correct Answer

✅ Option a — $\displaystyle 15$

All Options:

A $\displaystyle 15$
B $\displaystyle 20$
C $\displaystyle 25$
D $\displaystyle 8.30$

Detailed Solution & Explanation

We are given the quartiles of a variable: - First quartile (

\displaystyle Q_1

) =

\displaystyle 45

- Second quartile (Median,

\displaystyle Q_2

) =

\displaystyle 52

- Third quartile (

\displaystyle Q_3

) =

\displaystyle 75

The quartile deviation (Q.D.) is calculated as:

\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{75 - 45}{2} = \frac{30}{2} = 15

Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central Tendency Fiscal Policy vs Monetary Policy: CA Foundation Economics

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

The quartiles of a variable are 45\displaystyle 4545, 52\displaystyle 5252 and 75\displaystyle 7575 respectively. Its quartile deviation is