Question

The following data shows the score of seventh-grade students on a test:

Minimum value $=40$
Upper quartile $=70$
Inter-quartile range $=20$
Median $=60$
Maximum value $=80$

Choose the correct box and whiskers plot of the above data.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given:
Minimum value $=40$
Upper quartile $\left(Q_3\right)=70$
Inter-quartile range $=20$
Median $=60$
Maximum value $=80$

Plot meadian (60) as a second quartile and upper quartile (70)

Step 1: Find the lower quartile $\left(Q_1\right).$
We know that the inter-quartile range is the difference of the upper quartile and the lower quartile.

$\text{Inter-quartile range}=\text{Upper quartile}-\text{Lower quartile}$
$\Rightarrow 20=70-\text{Lower quartile}\left(Q_1\right)$
$\Rightarrow \text{Lower quartile}\left(Q_1\right)=70-20=50$

Step 2: Draw a box connecting $Q_1\left(50\right)$, $Q_2\left(60\right)$, and $Q_3\left(70\right)$

Step 3: Draw a whisker from the minimum$\left(40\right)$ to $Q_1\left(50\right)$ and from $Q_3\left(70\right)$ to the maximum$\left(80\right)$.

Hence, option (a.) is the correct choice.