# Here are the numbers of pages in the books on a reading list. 71 96 110 112 114 114 121 127 135 175 180 Which data values are outliers? Choose all answers that are correct.

##
71

96

175

180

71

96

175

180

##### 1 Answer

Jul 10, 2016

No extreme outlier.

#### Explanation:

- Data values are already sorted
#71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180# - Median assigned as
#Q_2=114# , Middle sample. - Lower quartile
#Q_1=110# , halfway point of the points in the data set below the median - Upper quartile
#Q_3=135# , halfway point of the points in the data set above the median - Interquartile range, the distance from
#Q_1" to "Q_3# is#(Q_3-Q_1)=135-110=25# - Inner fences for the data set
#="Interquartile range"xx1.5#

#=25xx1.5=37.5# . The boundaries of inner fence are#135+37.5=172.5, and#

# 110-37.5=72.5#

from inspection we see that data points#71, 175, 180# lie outside the range. These are mild outliers. - Outer fences for the data set
#="Interquartile range"xx3#

#=25xx3=75# . The boundaries of outer fence are#135+75=210, and#

# 110-75=35#

from inspection we see that no data point lie outside the range. There are no extreme outlier.