The US Census Bureau defines lower class as the lowest 20% of incomes.
Pew defines it as the lowest 2/3 of the median.
If the highest income is $100, 20% is $20.
At 2/3 the median, if the median is $30, lower-class is $20.
Is there a reason they’re tying income classes to people within those classes, and not what it costs to survive within the economy?
You can track things relating to those groups, though. Like if we consider the 20th percentile and below to be the very poorest in society, no matter how rich or poor society happens to be on average or what the wealth distribution is like - we can see how the very poorest fare in terms of education, health outcomes, etc over time.
Or like, looking at the median value - sure the amount of money the median-income worker has will change, but the median-income worker could afford a standard of living much closer to someone at the 90th percentile in 1960 than today’s median-income worker can.
Looking at things like this allows you to draw different comparisons.