Cowboys Refer to Exercise $80$

(a) Find and interpret the interquartile range (IQR).

(b) Determine whether there are any outliers. Show your work.

The table is

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 flier interquartile range (IQR) is calculated as$$\begin{gathered} Q_1=\frac{N+1}{4}thitem \\ {Q}_1=\frac{7+1}{4}thitem \\ {Q}_1=\frac{8}{4}thitem \\ {Q}_1=2thitem=303 \\ {Q}_3=\frac{3(N+1)}{4}thitem \\ {Q}_3=\frac{3(7+1)}{4}thitem \\ {Q}_3=\frac{24}{4}thitem \\ {Q}_3=6thitem=315 \\ IQR=Q_3-Q_1 \\ =315-303 \\ =12 \\ =12 \end{gathered}$$

Therefore, the flier interquartile range is $12$

We can conclude that there are no outliers in Joe's first $14$ quiz grades in a marking session. If an observation falls more than $1.5$ IQR above or below the First quartile, it is considered an outlier.$$\begin{gathered} IQR\times 1.5 \\ 12\times 1.5=18 \\ {Q}_1-18=303-18 \\ =285 \\ {Q}_3-18=315+18 \\ =333 \end{gathered}$$

There are no outliers because all of the items are within the range. Thus there are no outliers.