For this problem, we were given a certain dataset, as well as the quartiles Q1, Q, and Q3. From this information, we need to determine the lower and upper fences.
The fences are given by:
[tex]\begin{gathered} \text{lower}=Q_1-(1.5)\cdot\text{IQR} \\ \text{upper}=Q_3+(1.5)\cdot\text{IQR} \end{gathered}[/tex]Therefore, we need to calculate the value of the IQR, which is the subtraction between Q3 and Q1.
[tex]\begin{gathered} \text{IQR}=Q_3-Q_1=4.77-1.97 \\ \text{IQR}=2.8 \end{gathered}[/tex]With this, we have all the data to determine the lower and upper fences. The calculations are shown below:
[tex]\begin{gathered} \text{lower}=1.97-(1.5)\cdot2.8 \\ \text{lower}=-2.23 \\ \text{upper}=4.77+\cdot(1.5)\cdot2.8 \\ \text{upper}=8.97 \end{gathered}[/tex]Since there aren't any values that are lower than the lower fence or higher than the upper fence, we don't have any outlier on this data.
