Boxplots
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From the following boxplot
a) Determine the range
b) Determine the median
c) Determine the IQR
d) Is 5 an outlier? Explain your answer
\begin{align}
&\text { a) }\;\text{ Range }=5-1=4 \\
\\
&\text { b) }\;\text{ The median is the line in the box. } \\
&\qquad \therefore \text { Median }=3 \\
\\
&\begin{aligned}
\text { c) }\; IQR &=Q_{4}-Q_{2} \\
Q_{4} &=3.5, Q_{2}=1.5 \\
\therefore IQR &=3.5-1.5 \\
&=2
\end{aligned}\\
\\
&\begin{aligned}
\text { d) } \; \text{ Outlier} &\geq Q_{3}+1.5 \times IQR \\
Q_{3}=&3.5,\; IQR=2. \\
\therefore \text{ Outlier} & \geq 3.5+1.5 \times 2 \\
& \geq 6.5 \\
5 \ngeq 6.5& \therefore 5 \text { is not an outlier. }
\end{aligned}
\end{align}
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