If we have to generate a cumulative frequency table in the context of applying Newton's forward interpolation, how do we know when to construct the cumulative frequency table with lower interval and when to construct with upper interval.
For example, in the following problem, the table has been constructed with upper interval. We can similarly construct a table with lower bound. But this leads to widely different answers. Why?

When you construct the cumulative frequency table with lower bound, you will notice that there's an eerie similarity with Newton's backward difference approach.
With upper bound cumulative frequency, answer comes out to be 25. With lower bound cumulative frequency table, answer comes out to be 28.