Q 2.3. - The Practice of Statistics for AP

Question

The $2009$ roster of the Dallas Cowboys professional football team included 10 offensive linemen. Their weights (in pounds) were 

$338, 318, 353, 313, 318, 326, 307, 317, 311, 311$

Determine whether there are any outliers using the$1.5 \times \mathrm{IQR}$ rule.

Step-by-Step Solution

Answer

The higher outliner is$\mathbf{353}$

Step 1: Given information

Given data : 

$338, 318, 353, 313, 318, 326, 307, 317, 311, 311$

Step 2: Concept

$1.5$ times the interquartile range (IQR) (a constant used to discern outliers). To the third quartile, add $1.5\times \left(IQR\right)$. Any number higher than this is thought to be an aberration.

Step 3: Calculation

From (2.2), we have $IQR=15$

Thus, $$\begin{gathered} 1.5\times 15=22.5 \\ {Q}_3+22.5 \\ 326+22.5=348 \\ {Q}_1-22.5 \\ 311-22.5=288.5 \end{gathered}$$

Therefore, the higher outliner is$353$