Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 3113 of 473
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The relation between two variables is 2x−3y+12=0\displaystyle 2x - 3y + 12 = 0 If mean deviation of y\displaystyle y is 6\displaystyle 6 then mean deviation of x\displaystyle x is

Options

A9\displaystyle 9
B6\displaystyle 6
C3\displaystyle 3
DNone of these
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Correct Answer

✅ Option a — 9\displaystyle 9

All Options:

  • A9\displaystyle 9
  • B6\displaystyle 6
  • C3\displaystyle 3
  • DNone of these

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Detailed Solution & Explanation

We are given the relationship between variables x\displaystyle x and y\displaystyle y: 2x−3y+12=0  ⟹  2x=3y−12  ⟹  x=1.5y−62x - 3y + 12 = 0 \implies 2x = 3y - 12 \implies x = 1.5y - 6 Since mean deviation is independent of change of origin but affected by change of scale, the mean deviation of x\displaystyle x (M.D.x\displaystyle \text{M.D.}_x) is related to the mean deviation of y\displaystyle y (M.D.y\displaystyle \text{M.D.}_y) by: M.D.x=∣a∣×M.D.y\text{M.D.}_x = |a| \times \text{M.D.}_y Substitute the given values (a=1.5\displaystyle a = 1.5 and M.D.y=6\displaystyle \text{M.D.}_y = 6): M.D.x=1.5×6=9\text{M.D.}_x = 1.5 \times 6 = 9 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.

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