Q 101. - The Practice of Statistics for AP

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given information

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

Step 2: calculation

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.