Measures of Central Tendency and DispersionMCQMTP Nov 20Question 3104 of 473
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If the relation between x\displaystyle x and y\displaystyle y is 5y−3x=10\displaystyle 5y - 3x = 10 and the mean deviation about mean for x\displaystyle x is 12\displaystyle 12, then the mean deviation of y\displaystyle y about mean is

Options

A9.20\displaystyle 9.20
B6.80\displaystyle 6.80
C7.20\displaystyle 7.20
D15.80\displaystyle 15.80
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Correct Answer

✅ Option c — 7.20\displaystyle 7.20

All Options:

  • A9.20\displaystyle 9.20
  • B6.80\displaystyle 6.80
  • C7.20\displaystyle 7.20
  • D15.80\displaystyle 15.80

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Detailed Solution & Explanation

We are given the relationship between variables x\displaystyle x and y\displaystyle y: 5y−3x=10  ⟹  5y=3x+10  ⟹  y=0.6x+25y - 3x = 10 \implies 5y = 3x + 10 \implies y = 0.6x + 2 Since mean deviation is independent of change of origin but dependent on change of scale, for y=ax+b\displaystyle y = ax + b: M.D.y=∣a∣×M.D.x\text{M.D.}_y = |a| \times \text{M.D.}_x\n Substitute the given values (a=0.6\displaystyle a = 0.6 and M.D.x=12\displaystyle \text{M.D.}_x = 12): M.D.y=0.6×12=7.20\text{M.D.}_y = 0.6 \times 12 = 7.20 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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