Critique of Methods for Calculating Average Income Difference
An analyst is tasked with calculating the average income difference for a small community of six individuals. In this community, one person has a significantly higher income than the other five, who all share the same lower income. The absolute difference in income between the high-income individual and any one of the low-income individuals is $30.
The analyst proposes two different calculation methods:
Method 1: "The only meaningful differences are between the high-income person and the five low-income people. The ten pairs of low-income people all have a difference of zero, so they can be ignored. The average difference is therefore the total of the meaningful differences ($30 x 5 = $150) divided by the number of these meaningful pairs (5), resulting in an average difference of $30."
Method 2: "To find the average, we take the total sum of all pairwise differences ($30 x 5 = $150) and divide by the total number of people in the community (6), resulting in an average difference of $25."
Critique both methods. For each method, identify the specific conceptual error in its logic. Then, determine which method commits a more fundamental error in the context of calculating an average pairwise statistic, and justify your choice.
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