Answer:
The correct option is D. 3 is an outlier.
Step-by-step explanation:
A data set has outliers if the data lie out side the interval
[tex]I=[Q_1-1.5\times IQR,Q_3+1.5\times IQR][/tex]
The interquartile range of a data set is
[tex]IQR=Q_3-Q_1[/tex]
For option A, the required interval is [5.5, 25.5]. Since all the data lie in this interval, therefore this data set has no outliers.
For option B, the required interval is [-5, 19]. Since all the data lie in this interval, therefore this data set has no outliers.
For option C, the required interval is [-2.5, 17.5]. Since all the data lie in this interval, therefore this data set has no outliers.
For option D,
3, 6, 7, 7, 8, 8, 9, 9, 9, 10
(3, 6), 7, (7, 8),( 8, 9), 9,( 9, 10)
[tex]Q_1=7, Q_3=9[/tex]
[tex]IQR=Q_3-Q_1=9-7=2[/tex]
[tex]I=[Q_1-1.5\times IQR,Q_3+1.5\times IQR][/tex]
[tex]I=[7-1.5\times 2,9+1.5\times 2][/tex]
[tex]I=[7-3,9+3][/tex]
[tex]I=[4,12][/tex]
3 lies out side the interval [4,12]. It means this data set has an outlier, i.e,.
Therefore correct option is D.
