IQR and range

The times spent in minutes by 20 people waiting in a queue at the bank for a teller were:
3.4, 2.1, 3.8, 2.2, 4.5, 1.4, 0,0, 1.6, 4.8, 1.5, 1.9, 0, 3.6, 5.2, 2.7, 3.0, 0.8, 3.8, 5.2,
Find the range and interquartile range of the waiting times.

Correct answer:

r =  5.2
IQR =  2.4

Step-by-step explanation:

$$\begin{gathered} 3.4,2.1,3.8,2.2,4.5,1.4,0,0,1.6,4.8,1.5,1.9,0,3.6,5.2,2.7,3.0,0.8,3.8,5.2 \\ sort:0,0,0,0.8,1.4,1.5,1.6,1.9,2.1,2.2,2.7,3.0,3.4,3.6,3.8,3.8,4.5,4.8,5.2,5.2 \\ range=\max -min \\ r=5.2-0=5.2 \end{gathered}$$

$$\begin{gathered} n=20 \\ {i}_1=0.25\cdot n=0.25\cdot 20=5 \\ {i}_2=0.5\cdot n=0.5\cdot 20=10 \\ {i}_3=0.75\cdot n=0.75\cdot 20=15 \\ {Q}_1=1.4 \\ {Q}_2=2.2 \\ {Q}_3=3.8 \\ IQR=Q_3-Q_1=3.8-1.4=2.4 \end{gathered}$$

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