The QD of six numbers 13, 8, 36, 40, 38, 41 is equal to:

Option c: 13.5. Solution: We are given the observations: 13, 8, 36, 40, 38, 41 . 1. Arrange the data in ascending order: 8, 13, 36, 38, 40, 41 Here, the number of observations is n = 6 . 2. Find the first quartile ( Q1 ) and third quartile ( Q3 ) using the simplified method for small datasets: - Q1 = 13 (the second value). - Q3 = 40 (the fifth value). 3. Calculate the Quartile Deviation (Q.D.): Q.D. = Q3 - Q1/2 = 40 - 13/2 = 27/2 = 13.5 Hence, Option C is the correct answer.

The QD of six numbers $13, 8, 36, 40, 38, 41$ is equal to:

The correct answer is Option c: $13.5$. We are given the observations: $13, 8, 36, 40, 38, 41$. 1. Arrange the data in ascending order: $$8, 13, 36, 38, 40, 41$$ Here, the number of observations is $n = 6$. 2. Find the first quartile ($Q_1$) and third quartile ($Q_3$) using the simplified method for small datasets: - $Q_1 = 13$ (the second value). - $Q_3 = 40$ (the fifth value). 3. Calculate the Quartile Deviation (Q.D.): $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40 - 13}{2} = \frac{27}{2} = 13.5$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 22 Series IIQuestion 3247 of 473

All Questions

The QD of six numbers $\displaystyle 13, 8, 36, 40, 38, 41$ is equal to:

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 13, 8, 36, 40, 38, 41

. 1. Arrange the data in ascending order:

8, 13, 36, 38, 40, 41

Here, the number of observations is

\displaystyle n = 6

. 2. Find the first quartile (

\displaystyle Q_1

) and third quartile (

\displaystyle Q_3

) using the simplified method for small datasets: -

\displaystyle Q_1 = 13

(the second value). -

\displaystyle Q_3 = 40

(the fifth value). 3. Calculate the Quartile Deviation (Q.D.):

\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40 - 13}{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 QD of six numbers 13,8,36,40,38,41\displaystyle 13, 8, 36, 40, 38, 4113,8,36,40,38,41 is equal to: