Question

which measure of variability is not resistant to extreme values?
interquartile range
first quartile
range
third quartile

Explanation:

• Interquartile range: It is calculated as \(Q_3 - Q_1\) (where \(Q_1\) is the first quartile and \(Q_3\) is the third quartile). Since it only considers the middle 50% of the data, it is resistant to extreme values.
• First quartile (\(Q_1\)): It represents the 25th - percentile of the data. It is based on the lower - half of the ordered data set (excluding the extreme upper - end values in a non - resistant way for its calculation as it focuses on the lower portion). But it is not a measure of variability.
• Range: It is calculated as \( \text{Max}-\text{Min}\). If there is an extreme value (either a very large maximum or a very small minimum), the range will change significantly. For example, if we have a data set \(\{1,2,3,4\}\), the range is \(4 - 1=3\). If we add an extreme value like \(100\) to the data set \(\{1,2,3,4,100\}\), the range becomes \(100 - 1 = 99\).
• Third quartile (\(Q_3\)): It represents the 75th - percentile of the data. It is based on the upper - half of the ordered data set (excluding the extreme lower - end values in a non - resistant way for its calculation as it focuses on the upper portion). But it is not a measure of variability.

Answer:

range