Central Tendency & DispersionMTP March 22Question 3243 of 473

If the quartile deviation of $\displaystyle x$ is $\displaystyle 6$ and $\displaystyle 3x + 6y = 20$ , what is the quartile deviation of $\displaystyle y$ ?

\displaystyle 3

\displaystyle 4

\displaystyle 5

\displaystyle 6

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Correct Answer

✅ Option a — $\displaystyle 3$

We are given the relationship between variables

\displaystyle x

and

\displaystyle y

3x + 6y = 20 \implies 6y = -3x + 20 \implies y = -0.5x + \frac{10}{3}

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

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

Substitute the given values (

\displaystyle a = -0.5

and

\displaystyle \text{Q.D.}_x = 6

\text{Q.D.}_y = |-0.5| \times 6 = 0.5 \times 6 = 3

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

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