The IQR Is the interquartile range a resistant measure of spread? Give an example of a small data set that supports your answer.

The interquartile range (IQR) is a spread metric that is resistant to change.

Outliers have no effect on the range because it is a resistive measure of spread.

Take a look at the information below.

$1,2,3,4,5,6,7$

The median is the middle value of the sorted data collection since the number of data values is odd:

$MEDIAN=4$

The $Ist$quantile is the median of all data values below the median. The first quartile corresponds to the $2nd$data value since there are $3$values below the median in the data set.$Q_1=2$

Above the median, the median of all data values is the$3rd$quantile. Because there are 3 values above the median, the $3rd$quartile corresponds to the $6th$data value in the data set.$Q_3=6$

The interquartile range is the difference between the $3rd$and $Ist$quartiles.

$IQR=Q_3-Q_1=6-2=4$

When we change $7$to $100$, the IQR remains unchanged because the first and third quartiles remain unchanged. As a result, IQR is resistant.

As a result, the interquartile range is a spread metric that is resistant to change.