## Q. 3.36

Outliers

Check the following data set for outliers.

5, 6,12, 13, 15, 18, 22, 50

## Verified Solution

The data value 50 is extremely suspect. These are the steps in checking for an outlier.

Step 1 Find $Q_1$ and $Q_3 \cdot Q_1=\frac{(6+12)}{2}=9 ; Q_3=\frac{(18+22)}{2}=20$.

Step 2 Find the interquartile range (IQR), which is $Q_3-Q_1$.

$\mathrm{IQR}=Q_3-Q_1=20-9=11$

Step 3 Multiply this value by $1.5$.

$1.5(11)=16.5$

Step 4 Subtract the value obtained in step 3 from $Q_1$, and add the value obtained in step 3 to $Q_3$.

$9-16.5=-7.5 \qquad \text { and } \qquad 20+16.5=36.5$

Step 5 Check the data set for any data values that fall outside the interval from $-7.5$ to $36.5$. The value 50 is outside this interval; hence, it can be considered an outlier.