Question

In a survey, the mileage of cars in miles per gallon are collected, and represented in the following data set.

$20$

$18$

$19$

$28$

$24$

$26$

$22$

$21$

$23$

$27$

$20$

$25$

$26$

$23$

$28$

$24$

Which of the following box and whisker plot resembles the given data set?

• A.
• B.

Answer 1

The correct option is A

After arranging the given data set in ascending order, we get

$18$

$19$

$20$

$20$

$21$

$22$

$23$

$23$

$24$

$24$

$25$

$26$

$26$

$27$

$28$

$28$

From the above data set, we get
$\bullet$ lower extreme= $18$
$\bullet$ upper extreme= $28$
$\bullet$ middle quartile= median= mean of $23$ and $24$
$\Rightarrow$ middle quartile= $\frac{23+24}{2}=23.5$

$\bullet$ To calculate the lower quartile, we consider the left part of middle quartile $\left(23.5\right)$ data set.

$18$

$19$

$20$

$20$

$21$

$22$

$23$

$23$

Lower quartile= median of the just above data set= mean of $20$ and $21$
$\Rightarrow$ Lower quartile= $\frac{20+21}{2}=20.5$

$\bullet$ To calculate the upper quartile, we consider the right part of middle quartile $\left(23.5\right)$ data set.

$24$

$24$

$25$

$26$

$26$

$27$

$28$

$28$

Upper quartile= median of the just above data set= mean of $26$ and $26$
$\Rightarrow$ Upper quartile= $\frac{26+26}{2}=26$

To draw the box and whisker plot for the given data set, we follow the following steps:

1. Mark the lower and upper extremes, $18$ and $28$, respectively (dots in cyan).
2. Mark the middle quartile, $23.5$ (dot in green).
3. Mark lower and upper quartiles, $20.5$ and $26$, respectively (dots in orange).
4. Draw the box covering the lower and upper quartiles, i.e., between $20.5$ and $26$.
5. Extend the whiskers from the side of the box upto the lower and upper extremes, i,e., upto $18$ and $28$.

$\therefore$ The box and whisker plot in option (a.) is the correct representation of the given data.