Given data:
375, 210, 150, 147, 429, 189, 320, 580, 407, 180
First, rearrange the data from lowest to highest, and we get the data set
147, 150, 180, 189, 210, 320, 375, 407, 429, 580
[tex]\begin{gathered} \text{We have the following quartiles} \\ \\ Q_1=180 \\ Q_2=\frac{210+320}{2}=265 \\ Q_3=407 \end{gathered}[/tex]The IQR is determined by the formula
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ \text{substitute and we get} \\ IQR=407-180 \\ IQR=227 \end{gathered}[/tex]Therefore, the IQR of the data set is 227.
