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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? enter image description here

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.

yathish
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  • How much the answer var in two cases? it would be helpful to you if you could present the case of lower bound calculation! – BAYMAX Oct 08 '17 at 04:19
  • @BAYMAX I'm actually getting negative answer with lower bound cumulative frequency table approach which doesn't make sense – yathish Oct 08 '17 at 04:22
  • No problem,it would be helpful to you as potential users can identify the problem when you present what you have tried! go on and post it irrespective of whether answer is correct or not! – BAYMAX Oct 08 '17 at 04:24
  • @BAYMAX with lower bound answer is coming as 28. So now the question just remains as to which is a better interpolation.. – yathish Oct 08 '17 at 13:56

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