Question 3.36: Outliers Check the following data set for outliers. 5, 6,12,......

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.