Measures of Central Tendency and DispersionMCQMTP May 20Question 3085 of 473
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If Rx\displaystyle R_x and Ry\displaystyle R_y denote ranges of x\displaystyle x and y\displaystyle y respectively where x\displaystyle x and y\displaystyle y are related by 3x+2y+10=0\displaystyle 3x+2y+10=0, what would be the relation between x\displaystyle x and y\displaystyle y?

Options

ARx=Ry\displaystyle R_x = R_y
B2Rx=3Ry\displaystyle 2R_x = 3R_y
C3Rx=2Ry\displaystyle 3R_x = 2R_y
DRx=2Ry\displaystyle R_x = 2R_y
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Correct Answer

✅ Option c — 3Rx=2Ry\displaystyle 3R_x = 2R_y

All Options:

  • ARx=Ry\displaystyle R_x = R_y
  • B2Rx=3Ry\displaystyle 2R_x = 3R_y
  • C3Rx=2Ry\displaystyle 3R_x = 2R_y
  • DRx=2Ry\displaystyle R_x = 2R_y

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Detailed Solution & Explanation

We are given the linear relationship between variables x\displaystyle x and y\displaystyle y: 3x+2y+10=0  ⟹  2y=−3x−10  ⟹  y=−32x−53x + 2y + 10 = 0 \implies 2y = -3x - 10 \implies y = -\frac{3}{2}x - 5 Since range is independent of change of origin but affected by change of scale, for y=ax+b\displaystyle y = ax + b, the range is related by: Ry=∣a∣×RxR_y = |a| \times R_x Substitute a=−32\displaystyle a = -\frac{3}{2}: Ry=∣−32∣×Rx  ⟹  Ry=32Rx  ⟹  2Ry=3RxR_y = \left|-\frac{3}{2}\right| \times R_x \implies R_y = \frac{3}{2}R_x \implies 2R_y = 3R_x 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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