Question

If the quartile deviation of $x$ is $8$ and $3x+6y=20,$ then the quartile deviation of $y$ is

• A. $4$
• B. $3$
• C. $5$
• D. None of the above

Answer 1

The correct option is A $4$

if $y=a+bx$, $a$ and $b$ being constants, then

$QD$ of $y=$ $\left|b\right|\times$ $QD$ of $x$

Now,

$3x+6y=20$ (Given)

$6y=20-3x$

$\Rightarrow y=\frac{20}{6}-\frac{3x}{6}$

Frome the above equation,

$a=\frac{20}{6}$

$b=\frac{-3}{6}=\frac{-1}{2}\Rightarrow \left|b\right|=\frac{1}{2}$

QD of $x=8$ (Given)

$\therefore$ QD of $y=$ $\frac{1}{2}\times 8=4$