Answer:
The correct option is 3. The 10 foot wave is an outlier.
Step-by-step explanation:
The height of waves for 10 days are shown in the given figure.
From the figure it is noticed that the height of wave length is 2 for 5 days, 3 for 4 days and 10 for 1 day.
If arrange the height of wave in ascending order we get
[tex]2,2,2,2,2,3,3,3,3,10[/tex]
Total number of observation is 10.
[tex]Q_1=\frac{n}{4}\text{th term}[/tex]
[tex]Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}[/tex]
It means Q₁ is the average of second and third term.
[tex]Q_1=\frac{2+2}{2}=2[/tex]
[tex]Q_3=\frac{3n}{4}\text{th term}[/tex]
[tex]Q_3=\frac{3(10)}{4}\text{th term}=7.5\text{th term}[/tex]
It means Q₃ is the average of seventh and eight th term.
[tex]Q_3=\frac{3+3}{2}=3[/tex]
Interquartile range is the difference between Q₃ and Q₁.
[tex]I.Q.=Q_3-Q_1=3-2=1[/tex]
[tex]Q_1-1.5(I.Q.)=2-1.5=0.5[/tex]
[tex]Q_3+1.5(I.Q.)=3+1.5=4.5[/tex]
Therefore the data which lies outsides [tex][0.5,4.5][/tex] are outliers of the data.
Thus, the correct option is 3. The 10 foot wave is an outlier.
