Answer:
Only 71 is an outlier.
Step-by-step explanation:
The give data is
71, 84, 133, 140, 158, 166, 170, 171, 188, 198
Divide the data in two equal parts.
(71, 84, 133, 140, 158), (166, 170, 171, 188, 198)
Now, divide each parenthesis in two equal parts.
(71, 84), 133, (140, 158), (166, 170), 171, (188, 198)
It means first quartile is 133 and third quartile is 171.
The interquartile range is
\(IQR=Q_3-Q_1=171-133=38\)
If the data lies outside the range \([Q_1-1.5(IQR),Q_3+1.5(IQR)]\), then the data set has outliers.
\([Q_1-1.5(IQR),Q_3+1.5(IQR)]=[133-1.5(38),171+1.5(38)]\)
\([Q_1-1.5(IQR),Q_3+1.5(IQR)]=[76,228]\)
It means if the data lies outside the interval [76,228], then it is an outlier.
Since 71∉[76,228], therefore only 71 is an outlier.
