if a data set has only one outlier, which value will always change when the outlier is excluded?\n○ the…

Brief Explanations:

• Median: The median is the middle value (or average of two middle values) of a data set. If there's one outlier, unless the outlier is the middle value (unlikely for a single outlier in a typical data set), the median may not change. For example, in a data set with an odd number of values, removing an outlier at the end won't shift the middle position much.
• Range: The range is calculated as ( \text{Range} = \text{Maximum} - \text{Minimum} ). An outlier is typically an extreme value (either maximum or minimum in most cases). If we remove the outlier (say, the maximum), the new maximum will be lower, so the range will always change. For example, data set ( [1, 2, 3, 100] ): range is ( 100 - 1 = 99 ). Remove 100, new range is ( 3 - 1 = 2 ).
• Interquartile Range (IQR): IQR is ( Q_3 - Q_1 ), where ( Q_1 ) is the first quartile and ( Q_3 ) is the third quartile. Quartiles are based on the middle 50% of the data. A single outlier (outside the main cluster) doesn't affect the middle 50% much, so IQR usually remains the same.
• Upper Quartile (( Q_3 )): ( Q_3 ) is the median of the upper half of the data. A single outlier (if it's in the upper half but far out) might not be part of the upper half's median calculation (since the upper half is the data above ( Q_2 ) (median)). So removing a single outlier may not change ( Q_3 ).

Answer:

the range