Lets take an example that you are trying to evaluate average income of a company. Assume company has 100 employees in total and they belong to two stratum (70 management and 30 technical executives) and management executives on average are paid higher compared to technical executives.
You are the surveyor:
Due to resource constraints, you have access to survey of any 20 individuals chosen at random.
Case 1: you did a random sampling from 100 employees and end up with 10 management and 10 technical executives. you will get an estimate for average income that is biased towards technical executives. In other words, you are giving more importance/ representation to income of technical executives than
actual representation in the population.
Similarly, in other attempt:
Case 2: you did a random sampling from 100 employees and end up with 17 management and 3 technical executives. you will get an estimate for average income that is biased towards management executives.
Both the above sampled cases have bias and are not representative of the population. Therefore, when we have the stratum identified before the sampling, stratified sampling should be done. For eg. random sample for 14 out of 70 management executives and 6 out of 30 technical executives.
In your given example of the housing and income data, income scale has been shrunk by a factor of 1.5, so as to create less no of income categories for the same bin width. Any other factor > 1 could also be used to ensure each stratum has considerable number of instances.