We will use our Zillow data from before

38

60

60

70

90

101

250

Recall that we had:

Q1=60

Q2=70

Q3=101

\[\text{IQR}=Q3-Q1=101-60=41\]

So if we have an outlier the "rule of thumb" tells us that this data value will either be:

• More than \((1.5)\cdot\text{IQR}=(1.5)\cdot41=61.5\) below Q1, that is smaller than \(\text{Q1}-(1.5)\cdot\text{IQR}=60-61.5=-1.5\) but none of our data is that small.
• More than \((1.5)\cdot\text{IQR}=(1.5)\cdot41=61.5\) below Q3, that is bigger than \(\text{Q3}+(1.5)\cdot\text{IQR}=101+61.5=162.5\)... and notice that 250 IS bigger than that so it IS an outlier.

So our conclusion is that the data value of 250 is an outlier