Question

why might we have seen such a large divergence in the median and mean incomes in the 2010 to 2013 period, with one increasing and the other decreasing? figure 1. change in median and mean family incomes, 2010 - 16 surveys click or tap a choice to answer the question. inflation caused the working class to have less disposable income than high - income earners. tax increases hit the wealthy harder during this time period than they did the middle class. while most people saw their income decrease, a small number of very high - income earners saw their income increase. income inequality narrowed during this time period, with people in the middle of the income distribution doing better than people at the extremes.

Explanation:

The median is the middle - value in a data set. The mean is the average of all values. If most people's incomes decrease (pulling the median down) but a small number of very high - income earners see their income increase (pulling the mean up), this can cause the divergence. For example, if we have a data set of incomes \(\{1,2,3\}\), the median is \(2\) and the mean is \(\frac{1 + 2+3}{3}=2\). If we change the data set to \(\{1,2,10\}\), the median is \(2\) (unchanged if the number of data points is odd and the middle value is not affected by the extreme value) and the mean is \(\frac{1 + 2 + 10}{3}=\frac{13}{3}\approx4.33\).

Answer:

While most people saw their income decrease, a small number of very high - income earners saw their income increase.