# 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

Jul 10, 2016

$71 , 175 , 180$ 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 ${Q}_{1} \text{ to } {Q}_{3}$ is $\left({Q}_{3} - {Q}_{1}\right) = 135 - 110 = 25$
7. Inner fences for the data set $= \text{Interquartile range} \times 1.5$
$= 25 \times 1.5 = 37.5$. The boundaries of inner fence are $135 + 37.5 = 172.5 , \mathmr{and}$
$110 - 37.5 = 72.5$
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 $= \text{Interquartile range} \times 3$
$= 25 \times 3 = 75$. The boundaries of outer fence are $135 + 75 = 210 , \mathmr{and}$
$110 - 75 = 35$
from inspection we see that no data point lie outside the range. There are no extreme outlier.