Question

Data sets for two quantities $X$ and $Y$ are represented in the following box and whiskers plots.


Quantity is relatively more spreaded than quantity .

• A. $X$
• B. $Y$
• C. $X\times Y$
• D. $\frac{X}{Y}$

Answer 1

Answer: (A), (B)

$Y$

Let's find out the extremes and quartiles for the two quantities $X$ and $Y$:

	$X$	$Y$
Lower extreme	$25$	$20$
Upper extreme	$70$	$80$
Lower quartile	$35$	$40$
Middle quartile	$50$	$50$
Upper quartile	$65$	$60$

$\bullet$ Inter-quartile range for the quantity $X$
$=\text{Upper quartile}-\text{Lower quartile}$
$=65-35=30$

$\bullet$ Inter-quartile range for the quantity $Y$
$=\text{Upper quartile}-\text{Lower quartile}$
$=60-40=20$

As the inter-quartile range of the quantity $X$ is greater than the inter-quartile range of quantity $Y$, the data in $X$ is more spreaded around the median or middle quartile as compare to the quantity $Y$.

$\therefore$ Quantity $X$ is relatively more spreaded than the quantity $Y$.