Question

Choose the correct box and whiskers plot for the following data set.

$23$

$46$

$71$

$83$

$65$

$56$

$21$

$19$

$73$

$8$

$6$

• A.
• B.
• C. None of the above

Answer 1

The correct option is B

First, we arrange the data set in an ascending order.

$\underset{–}{6}$

$8$

$19$

$21$

$23$

$\underset{–}{46}$

$56$

$65$

$71$

$73$

$\underset{–}{83}$

From the above data set, we get
$\bullet$ lower extreme: $6$
$\bullet$ upper extreme: $83$
$\bullet$ middle quartile= median of the data set= $46$

Let's consider the left data points of middle quartile:

$6$

$8$

$\underset{–}{19}$

$21$

$23$

$\bullet$ Lower quartile= median of the just above data set= $19$

For calculating the upper quartile, consider the right data points of middle quartile:

$56$

$65$

$\underset{–}{71}$

$73$

$83$

$\bullet$ Upper quartile= median of the just above data set= $71$

To draw the box and whiskers plot, we can follow the following steps:

1. Mark the lower and upper extremes.
2. Mark the middle, lower and upper quartiles.
3. Construct a box between the lower and upper quartiles.
4. Extend the whiskers till the lower and upper extremes starting from the box.

$\therefore$ The box and whiskers plot in option (b.) is the correct representation of the given data set.