Chapter 1.3, Problem 101E

To determine

To explain: whether the interquartile range is a resistant measure of spread.

Answer to Problem 101E

Yes, the interquartile range is a resistant measure of spread

Explanation of Solution

Given:

Interquartile range

Calculation:

The range is a resistant measure of spread, thus it is unaffected by outliers.

Take the following data list

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

Since the number of data values is odd, the median is the middle value of the sorted data set:

  $MEDIAN=4$

The first quantile is the median of all data values below the median. Since the data set contains 3 values below the median, the first quartile is then the 2 th data value.$Q_1=2$

The third quantile is the median of all data values above the median. Since the data set contains 3 values above the median, the third quartile is then the 6 th data value.$Q_3=6$

The interquartile range is the difference between the third and the first quartile:

  $IQR=Q_3-Q_1=6-2=4$

If we change the 7 to 100, then we note that the IQR will not change, because the first and third quartile does not change. Thus IQR is resistant.

Conclusion:

Therefore,the interquartile range is a resistant measure of spread