Central Tendency & DispersionMTP 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

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.

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