Central Tendency & DispersionMTP Oct 21Question 3242 of 473
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In the equation 4x+2y=3\displaystyle 4x + 2y = 3, quartile deviation for y\displaystyle y is 3\displaystyle 3. Find the quartile deviation for x\displaystyle x.

Options

A4.5\displaystyle 4.5
B6\displaystyle 6
C1.5\displaystyle 1.5
DNone of these
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Correct Answer

✅ Option c — 1.5\displaystyle 1.5

All Options:

  • A4.5\displaystyle 4.5
  • B6\displaystyle 6
  • C1.5\displaystyle 1.5
  • DNone of these

Detailed Solution & Explanation

We are given the relationship between variables x\displaystyle x and y\displaystyle y: 4x+2y=3  ⟹  4x=−2y+3  ⟹  x=−0.5y+0.754x + 2y = 3 \implies 4x = -2y + 3 \implies x = -0.5y + 0.75 Since quartile deviation is independent of change of origin but affected by change of scale: Q.D.x=∣a∣×Q.D.y\text{Q.D.}_x = |a| \times \text{Q.D.}_y Substitute the given values (a=−0.5\displaystyle a = -0.5 and Q.D.y=3\displaystyle \text{Q.D.}_y = 3): Q.D.x=∣−0.5∣×3=0.5×3=1.5\text{Q.D.}_x = |-0.5| \times 3 = 0.5 \times 3 = 1.5 Hence, **Option C** is the correct answer.

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