Outliers
Check the following data set for outliers.
5, 6,12, 13, 15, 18, 22, 50
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.