Question

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

Answer 1

`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.