91Ó°ÊÓ

• The range is the difference between the largest observation and the smallest observation of a data set.
• The median is the middle value when a data set is ordered from least to greatest. It is the second quartile (Q₂) and divides the data into two half.

• The lower quartile Q₁is the median of the lower half of the data.
• The upper quartile Q₃ is the median of the upper half of the data.

Given:

{16,19,21,24,25,31,35}.

Arrange the data set in ascending order:

16,19,21,24,25,31,35

$\begin{array}{l}Range=L\arg est−Smallest\\ ⇒Range=35−16\\ ⇒Range=19\end{array}$

Given:

{16,19,21,24,25,31,35}.

Arrange the data set in ascending order:

16,19,21,24,25,31,35

So, the median is the average of ${\left(\frac{7+1}{2}\right)}^{th}=4^{th}$observation

Therefore, the median is $Q_2=24$.

Given:

{16,19,21,24,25,31,35}.

Arrange the data set in ascending order:

16,19,21,24,25,31,35

From step 3, the median of the data set is 24 and the data set is odd

Hence, the lower half of the data set is :

16,19,21

The lower quartile is the median of the lower half of the data set:

$Q_1=19$

Given:

{16,19,21,24,25,31,35}.

Arrange the data set in ascending order:

16,19,21,24,25,31,35

From step 3, the median of the data set is 24 and the data set is odd

Hence, the upper half of the data set is:

25,31,35

The upper quartile is the median of the upper half of the data set:

$⇒Q_3=31$