Question

Choose the correct option with respect to the box and whiskers plot.

Statement I: The median of a data set is called the middle quartile.

Statement II: The medians which give the lower and upper 25% of the data set are called lower quartile and upper quartile, respectively.

Statement III: The lower and upper extremes are the lowest and the highest data points, respectively.

• A. Only statement I is correct.
• B. Only statement I and II are correct.
• C. All the statements are correct.
• D. All the statements are incorrect.

Answer 1

The correct option is C All the statements are correct.

$\underset{–}{\text{Middle Quartile}}$
Middle value which is the median of the data set

$\therefore$ Statement I is correct.

$\underset{–}{\text{Lower Quartile}}$
The median that gives us the lower 25% of the data set

$\underset{–}{\text{Upper Quartile}}$
The median that gives us the upper 25% of the data set

$\therefore$ Statement II is correct.

$\underset{–}{\text{Lower Extreme}}$
The lowest data point in the data set

​​​​​​​$\underset{–}{\text{Upper Extreme}}$
The highest data point in the data set

$\therefore$ Statement III is correct.

Let's consider the below arranged data set:

$0$

$1$

$1$

$2$

$\underset{–}{3}$

$6$

$7$

$8$

$9$

Number of data points in the data set= $9$
$\therefore \text{Middle quartile = median}=3$

The lower quartile is the median of the part of the data set which is left to the middle quartile.

$\therefore \text{Lower quartile}=\text{median of}\{0,1,1,2\}$
$=\frac{1+1}{2}=\frac{2}{2}=1$, which gives us the lower 25% of the data set, i.e., $\{0,1\}$

The upper quartile is the median of the part of the data set which is right to the middle quartile.

$\therefore \text{Upper quartile}=\text{median of}\{6,7,8,9\}$
$=\frac{7+8}{2}=\frac{15}{2}=7.5$, which gives us the upper 25% of the data set, i.e., $\{8,9\}$

The lowest and the highest values in a data set are called the lower and upper extremes, respectively.

$\therefore$ Lower extreme= $0$, and
upper extreme= $9$

$\therefore$ All statements I, II and III are correct.