If Quartile deviation is 7 . Find the value of x from the arranged series: 2, x, 6, 7, 9, 16, 18 .

Option b: 2. Solution: We are given an arranged series: 2, x, 6, 7, 9, 16, 18 with n = 7 . - The first quartile ( Q1 ) is the second value: Q1 = x . - The third quartile ( Q3 ) is the sixth value: Q3 = 16 . - Quartile deviation (Q.D.) = 7 . Set up the quartile deviation equation: Q.D. = Q3 - Q1/2 7 = 16 - x/2 14 = 16 - x x = 2 Hence, Option B is the correct answer.

If Quartile deviation is $7$. Find the value of $x$ from the arranged series: $2, x, 6, 7, 9, 16, 18$.

The correct answer is Option b: $2$. We are given an arranged series: $2, x, 6, 7, 9, 16, 18$ with $n = 7$. - The first quartile ($Q_1$) is the second value: $Q_1 = x$. - The third quartile ($Q_3$) is the sixth value: $Q_3 = 16$. - Quartile deviation (Q.D.) = $7$. Set up the quartile deviation equation: $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} \implies 7 = \frac{16 - x}{2}$$ $$14 = 16 - x \\implies x = 2$$ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 23 - Series IQuestion 3259 of 473

All Questions

If Quartile deviation is $\displaystyle 7$ . Find the value of $\displaystyle x$ from the arranged series: $\displaystyle 2, x, 6, 7, 9, 16, 18$ .

Options

\displaystyle 5

\displaystyle 2

\displaystyle 8

\displaystyle 6

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Correct Answer

✅ Option b — $\displaystyle 2$

All Options:

A $\displaystyle 5$
B $\displaystyle 2$
C $\displaystyle 8$
D $\displaystyle 6$

Detailed Solution & Explanation

We are given an arranged series:

\displaystyle 2, x, 6, 7, 9, 16, 18

with

\displaystyle n = 7

. - The first quartile (

\displaystyle Q_1

) is the second value:

\displaystyle Q_1 = x

. - The third quartile (

\displaystyle Q_3

) is the sixth value:

\displaystyle Q_3 = 16

. - Quartile deviation (Q.D.) =

\displaystyle 7

. Set up the quartile deviation equation:

\text{Q.D.} = \frac{Q_3 - Q_1}{2} \implies 7 = \frac{16 - x}{2}

14 = 16 - x \\implies x = 2

Hence, **Option B** 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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If Quartile deviation is 7\displaystyle 77. Find the value of x\displaystyle xx from the arranged series: 2,x,6,7,9,16,18\displaystyle 2, x, 6, 7, 9, 16, 182,x,6,7,9,16,18.