Respuesta :
Given the following speed in radar below,
[tex]61,65,67,68,68,70,77,80,87,88,103,105[/tex]To find the first quartile, Q₁ below, where N = 12
[tex]Q_1=(\frac{N+1}{4})^{th}_{}=(\frac{13}{4})^{th}=3.25^{th}[/tex]Hence, Q₁ = 68
To find the second quartile, Q₂, where N = 12,
[tex]\begin{gathered} ^{}Q_2=\lbrack2(\frac{N+1}{4})\rbrack^{th}=\lbrack2(\frac{12+1}{4})\rbrack^{th}=\lbrack2(\frac{13}{4})\rbrack^{th}=\lbrack\frac{26}{4}\rbrack^{th}=6.5^{th} \\ \end{gathered}[/tex]Since the median lies between the 6th and 7th data, hence Q₂ is,
[tex]Q_2=\frac{70+77}{2}=\frac{147}{2}=73.5[/tex]Hence, Q₂ = 73.5
To find the third quartile, Q₃, where N = 12,
[tex]Q_3=\lbrack3(\frac{N+1}{4})\rbrack^{th}=\lbrack3\times3.25\rbrack^{th}=9.75^{th}[/tex]Hence, Q₃ = 88
To find the Interquartile range (IQR),
[tex]\begin{gathered} IQR=Q_3-Q_1=88-68=20 \\ \text{IQR = 20} \end{gathered}[/tex]Hence, IQR = 20
