Measures of Central Tendency and DispersionMCQMTP Nov 20Question 3239 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 16\displaystyle 16, then the QD of y\displaystyle y is

Options

A16\displaystyle 16
B14\displaystyle 14
C10\displaystyle 10
D12\displaystyle 12
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Correct Answer

✅ Option d — 12\displaystyle 12

All Options:

  • A16\displaystyle 16
  • B14\displaystyle 14
  • C10\displaystyle 10
  • D12\displaystyle 12

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Detailed Solution & Explanation

We are given the linear relationship between variables x\displaystyle x and y\displaystyle y: 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=16\displaystyle \text{Q.D.}_x = 16): Q.D.y=∣−0.75∣×16=0.75×16=12\text{Q.D.}_y = |-0.75| \times 16 = 0.75 \times 16 = 12 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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