Respuesta :
Answer:
(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]
(b) [tex]IQR=9.5[/tex]
(c) 15
Step-by-step explanation:
The given data set is
41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30
Arrange the data in ascending order.
15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55
Divide the data in four equal parts.
(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)
Now,
[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]
[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]
[tex]Q_3=\dfrac{44+48}{2}=46[/tex]
[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]
Range for outlier is
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]
[tex]=[22.25,60.25][/tex]
Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.
