Question

which statement is true?
both the range and iqr are affected by outliers
neither the range nor the iqr are affected by outliers
the iqr is not as affected by outliers as the range
the range is not as affected by outliers as the iqr

Explanation:

The range is calculated as \( \text{Range} = \text{Max}-\text{Min}\). If there is an outlier (either a very large or very small value), the max or min (and thus the range) changes. The inter - quartile range (IQR) is \( \text{IQR}=Q_3 - Q_1\), where \(Q_1\) is the first quartile (25th percentile) and \(Q_3\) is the third quartile (75th percentile). Quartiles are based on the position of data points in an ordered data set. Outliers at the extremes of the data set do not affect the position of \(Q_1\) and \(Q_3\) as much as they affect the max and min values. So, the IQR is more robust (less affected) by outliers compared to the range.

Answer:

C. The IQR is not as affected by outliers as the range