If in a data set, 25 percent of values are smaller than 30 and one-fourth of values are larger than 70 , then the coefficient of quartile deviation is %

Option a: 40. Solution: We are given: - 25% of values are smaller than 30 the first quartile ( Q1 ) is 30 . - One-fourth ( 25% ) of values are larger than 70 the remaining 75% are smaller than 70 , which means the third quartile ( Q3 ) is 70 . Calculate the coefficient of quartile deviation: Coefficient of Q.D. = Q3 - Q1/Q3 + Q1 × 100 Coefficient of Q.D. = 70 - 30/70 + 30 × 100 = 40/100 × 100 = 40% Hence, Option A is the correct answer.

If in a data set, $25$ percent of values are smaller than $30$ and one-fourth of values are larger than $70$, then the coefficient of quartile deviation is _________ %

The correct answer is Option a: $40$. We are given: - $25\%$ of values are smaller than $30 \implies$ the first quartile ($Q_1$) is $30$. - One-fourth ($25\%$) of values are larger than $70 \implies$ the remaining $75\%$ are smaller than $70$, which means the third quartile ($Q_3$) is $70$. Calculate the coefficient of quartile deviation: $$\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100$$ $$\text{Coefficient of Q.D.} = \frac{70 - 30}{70 + 30} \times 100 = \frac{40}{100} \times 100 = 40\%$$ Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ June 24Question 3230 of 473

All Questions

If in a data set, $\displaystyle 25$ percent of values are smaller than $\displaystyle 30$ and one-fourth of values are larger than $\displaystyle 70$ , then the coefficient of quartile deviation is _________ %

Options

\displaystyle 40

\displaystyle 30

\displaystyle 70

\displaystyle 50

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Correct Answer

✅ Option a — $\displaystyle 40$

All Options:

A $\displaystyle 40$
B $\displaystyle 30$
C $\displaystyle 70$
D $\displaystyle 50$

Detailed Solution & Explanation

We are given: -

\displaystyle 25\%

of values are smaller than

\displaystyle 30 \implies

the first quartile (

\displaystyle Q_1

) is

\displaystyle 30

. - One-fourth (

\displaystyle 25\%

) of values are larger than

\displaystyle 70 \implies

the remaining

\displaystyle 75\%

are smaller than

\displaystyle 70

, which means the third quartile (

\displaystyle Q_3

) is

\displaystyle 70

. Calculate the coefficient of quartile deviation:

\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100

\text{Coefficient of Q.D.} = \frac{70 - 30}{70 + 30} \times 100 = \frac{40}{100} \times 100 = 40\%

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.

Key Concepts to Understand

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

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If in a data set, 25\displaystyle 2525 percent of values are smaller than 30\displaystyle 3030 and one-fourth of values are larger than 70\displaystyle 7070, then the coefficient of quartile deviation is _________ %