Central Tendency & DispersionMTP June 2023 Series IQuestion 3261 of 473

If $\displaystyle X$ and $\displaystyle Y$ are related as $\displaystyle 3X - 4Y = 20$ and the quartile deviation of $\displaystyle X$ is $\displaystyle 12$ , then the quartile deviation of $\displaystyle Y$ is:

\displaystyle 14

\displaystyle 15

\displaystyle 16

\displaystyle 9

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Correct Answer

✅ Option d — $\displaystyle 9$

We are given variables

\displaystyle x

and

\displaystyle y

related by:

3x - 4y = 20 \implies 4y = 3x - 20 \implies y = 0.75x - 5

Since quartile deviation is independent of change of origin but affected by change of scale, the relationship is:

\text{Q.D.}_y = |a| \times \text{Q.D.}_x

Substitute the given values (

\displaystyle a = 0.75

and

\displaystyle \text{Q.D.}_x = 12

\text{Q.D.}_y = 0.75 \times 12 = 9

Hence, **Option D** is the correct answer.

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