Central Tendency & DispersionMTP Dec 23 Series IIQuestion 3111 of 473

If the relation between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 4y - 3x = 10$ and the mean deviation about mean for $\displaystyle x$ is $\displaystyle 12$ , then the mean deviation of $\displaystyle y$ about mean is

\displaystyle 9.00

\displaystyle 7.80

\displaystyle 12.3

DNone of these

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Correct Answer

✅ Option a — $\displaystyle 9.00$

We are given the relationship between

\displaystyle x

and

\displaystyle y

4y - 3x = 10 \implies 4y = 3x + 10 \implies y = 0.75x + 2.5

Since mean deviation is independent of change of origin but dependent on change of scale:

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

Substitute the given values (

\displaystyle a = 0.75

and

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

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

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

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