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

1 Answer
Jul 10, 2016

Answer:

#71, 175, 180# are mild outliers
No extreme outlier.

Explanation:

  1. Data values are already sorted
  2. #71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180#
  3. Median assigned as #Q_2=114#, Middle sample.
  4. Lower quartile #Q_1=110#, halfway point of the points in the data set below the median
  5. Upper quartile #Q_3=135#, halfway point of the points in the data set above the median
  6. Interquartile range, the distance from #Q_1" to "Q_3# is #(Q_3-Q_1)=135-110=25#
  7. 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.
  8. 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.