Question

In box and whiskers plot, the represent the extreme points, whereas the represents the $50\%$ of the data points.

• A. whiskers
• B. box
• C. mean
• D. median

Answer 1

Answer: (A), (B)

box

Let's consider the following data set:

$9$

$0$

$1$

$3$

$2$

$1$

$7$

$6$

$8$

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

$\underset{–}{0}$

$1$

$1$

$2$

$\underset{–}{3}$

$6$

$7$

$8$

$\underset{–}{9}$

In the above ordered data set,
$\bullet$ Median= $3$
$\bullet$ Smallest value= $0$
$\bullet$ Largest value= $9$

$\underset{–}{\text{Note:}}$ Median is a measure of central tendency that divides the data set into two equal halves, when arranged in order.

Now, the median of lower half data set, i.e., median of $\{0,1,1,2\}$ is
$\frac{1+1}{2}=\frac{2}{2}=1$

Next, the median of upper half data set, i.e., median of $\{6,7,8,9\}$ is
$\frac{7+8}{2}=\frac{15}{2}=7.5$

Box and whiskers plot of the data set is as follows:


Where,
$3\text{(point in orange)}:\text{Median}$
$0,9\text{(points in cyan)}:\text{Extremes}$
$1,7.5\text{(points in green)}:\text{Quartiles}$

$\underset{–}{\text{Quartiles:}}$ Numbers that divide a collection of data into four intervals each of which has the same number of data points.

In the box and whiskers plot, the box represents the half of the data points, i.e., the data points between $1$ and $7.5$, and the respective data points are $\{2,3,6,7\}$

Whereas the extended whiskers represent the extreme points, i.e., $0$ and $9$.