The Q.D of 6 numbers 15, 8, 36, 40, 38, 41 is

Option c: 13.5. Solution: We are given the observations: 15, 8, 36, 40, 38, 41 . 1. Arrange the data in ascending order: 8, 15, 36, 38, 40, 41 Here, the number of observations is n = 6 . 2. Find the first quartile ( Q1 ): - Position of Q1 = 6+1/4 = 1.75th term. - Q1 = 8 + 0.75 × (15 - 8) = 13.25 . 3. Find the third quartile ( Q3 ): - Position of Q3 = 3(6+1)/4 = 5.25th term. - Q3 = 40 + 0.25 × (41 - 40) = 40.25 . 4. Calculate Quartile Deviation (Q.D.): Q.D. = Q3 - Q1/2 = 40.25 - 13.25/2 = 27/2 = 13.5 Hence, Option C is the correct answer.

The Q.D of $6$ numbers $15, 8, 36, 40, 38, 41$ is

The correct answer is Option c: $13.5$. We are given the observations: $15, 8, 36, 40, 38, 41$. 1. Arrange the data in ascending order: $$8, 15, 36, 38, 40, 41$$ Here, the number of observations is $n = 6$. 2. Find the first quartile ($Q_1$): - Position of $Q_1 = \frac{6+1}{4} = 1.75^{\text{th}}$ term. - $Q_1 = 8 + 0.75 \times (15 - 8) = 13.25$. 3. Find the third quartile ($Q_3$): - Position of $Q_3 = \frac{3(6+1)}{4} = 5.25^{\text{th}}$ term. - $Q_3 = 40 + 0.25 \times (41 - 40) = 40.25$. 4. Calculate Quartile Deviation (Q.D.): $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40.25 - 13.25}{2} = \frac{27}{2} = 13.5$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ June 19Question 3217 of 473

All Questions

The Q.D of $\displaystyle 6$ numbers $\displaystyle 15, 8, 36, 40, 38, 41$ is

Options

\displaystyle 12.5

\displaystyle 25

\displaystyle 13.5

\displaystyle 37

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Correct Answer

✅ Option c — $\displaystyle 13.5$

All Options:

A $\displaystyle 12.5$
B $\displaystyle 25$
C $\displaystyle 13.5$
D $\displaystyle 37$

Detailed Solution & Explanation

We are given the observations:

\displaystyle 15, 8, 36, 40, 38, 41

. 1. Arrange the data in ascending order:

8, 15, 36, 38, 40, 41

Here, the number of observations is

\displaystyle n = 6

. 2. Find the first quartile (

\displaystyle Q_1

): - Position of

\displaystyle Q_1 = \frac{6+1}{4} = 1.75^{\text{th}}

term. -

\displaystyle Q_1 = 8 + 0.75 \times (15 - 8) = 13.25

. 3. Find the third quartile (

\displaystyle Q_3

): - Position of

\displaystyle Q_3 = \frac{3(6+1)}{4} = 5.25^{\text{th}}

term. -

\displaystyle Q_3 = 40 + 0.25 \times (41 - 40) = 40.25

. 4. Calculate Quartile Deviation (Q.D.):

\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40.25 - 13.25}{2} = \frac{27}{2} = 13.5

Hence, **Option C** 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.

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The Q.D of 6\displaystyle 66 numbers 15,8,36,40,38,41\displaystyle 15, 8, 36, 40, 38, 4115,8,36,40,38,41 is