Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 3261 of 473
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If X\displaystyle X and Y\displaystyle Y are related as 3X−4Y=20\displaystyle 3X - 4Y = 20 and the quartile deviation of X\displaystyle X is 12\displaystyle 12, then the quartile deviation of Y\displaystyle Y is:

Options

A14\displaystyle 14
B15\displaystyle 15
C16\displaystyle 16
D9\displaystyle 9
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Correct Answer

✅ Option d — 9\displaystyle 9

All Options:

  • A14\displaystyle 14
  • B15\displaystyle 15
  • C16\displaystyle 16
  • D9\displaystyle 9

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Detailed Solution & Explanation

We are given variables x\displaystyle x and y\displaystyle y related by: 3x−4y=20  ⟹  4y=3x−20  ⟹  y=0.75x−53x - 4y = 20 \implies 4y = 3x - 20 \implies y = 0.75x - 5 Since quartile deviation is independent of change of origin but affected by change of scale, the relationship is: Q.D.y=∣a∣×Q.D.x\text{Q.D.}_y = |a| \times \text{Q.D.}_x Substitute the given values (a=0.75\displaystyle a = 0.75 and Q.D.x=12\displaystyle \text{Q.D.}_x = 12): Q.D.y=0.75×12=9\text{Q.D.}_y = 0.75 \times 12 = 9 Hence, **Option D** 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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