Q 2.2. - 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 

Calculate the IQR. Interpret this value in the context

Step-by-Step Solution

Answer

The IQR is 15

Step 1: Given information

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

Step 2: Concept

The interquartile range describes the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal sections by quartiles. The second and third quartiles, or the centre half of your data set, make up the interquartile range (IQR).

Step 3: Explanation

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

No. of observations: $10$

Following the arrangement of the given data in ascending order:

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

Now divides the list into two parts:

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

Because each half has five values, finding the sub medians, or first and third quartiles is simple. 

So ${Q }_1= 311$ and the minimum: $Q_3 : 326$

IQR is calculated as: $Q_3 -{ Q }_1= IQR$

After you've entered all of the values,

$326 - 311 = 15$

Thus, $IQR = 15$