Central Tendency & DispersionMTP June 2023 Series IQuestion 2983 of 473
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The relationship between two variable x\displaystyle x and y\displaystyle y is given by 4x−10y=20\displaystyle 4x - 10y = 20. If the median value of the variable x\displaystyle x is 20\displaystyle 20 then what is median value of variable y\displaystyle y?

Options

A1.0\displaystyle 1.0
B2.0\displaystyle 2.0
C3.0\displaystyle 3.0
D6.0\displaystyle 6.0
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Correct Answer

✅ Option d — 6.0\displaystyle 6.0

All Options:

  • A1.0\displaystyle 1.0
  • B2.0\displaystyle 2.0
  • C3.0\displaystyle 3.0
  • D6.0\displaystyle 6.0

Detailed Solution & Explanation

We are given the relationship between two variables x\displaystyle x and y\displaystyle y: 4x−10y=204x - 10y = 20 Since partition values satisfy linear transformations directly, we can substitute the median value of x\displaystyle x (which is 20\displaystyle 20) to find the median value of y\displaystyle y: 4(Medianx)−10(Mediany)=204(\text{Median}_x) - 10(\text{Median}_y) = 20 4(20)−10(Mediany)=204(20) - 10(\text{Median}_y) = 20 80−10(Mediany)=2080 - 10(\text{Median}_y) = 20 10(Mediany)=60  ⟹  Mediany=6.010(\text{Median}_y) = 60 \implies \text{Median}_y = 6.0 Hence, **Option D** is the correct answer.

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