Examples of Newton Interpolation
Example No 1: The following supply schedule gives the quantity supplied in hundreds of a product at prices in rupees:

80 
90 
100 
110 
120 

25 
30 
42 
50 
68 
Interpolate, what will be the quantity supplied of the product at a price Dollor 85.
Solution: Constructing the difference table first.
THE DIFFERENCE TABLE








80 
25 
5 
7 
11 
25 
90 
30 
12 
4 
14 

100 
42 
8 
10 


110 
50 
18 



120 
68 






43 
13 
3 
25 
On checking, we found that the table is correctly prepared, now, we have
Also
We may either put in the formula, but the latter is subject to errors due to misleading of the decimal point in multiplication.
Now, using formula and substituting the corresponding values, we have
Now determine the sign of each term by the same rule given earlier, i.e. count the number of negative signs and place a negative sign before the term, if the number of negative signs are odd, and a positive sign before the term if the number of negative signs are even, then forget the individual signs.
Cancel the common factors, if any, in each term and simplify
Example No 2: The production of vegetable oil is recorded on a fiscal – year basis alternate years:
Year:

1990 – 91 
1992 – 93 
1994 – 95 
1996 – 97 
1998 – 99 
Production 
35.5 
42.8 
45.8 
46.5 
50.3 
Estimate the production during 1997 – 98.
Solution: In this situation again we can multiply the values in the second column by 10, and the adjustment may be made in the final answer by dividing the result by 10.
Another problem will arise hare as to which should be regarded as and . The equal class interval is obvious and that is 2. The value of may be determined by either considering the lower limits of the years or by considering the upper limits of the years. Thus, in order to calculate the value of from Newton formula of interpolation, we can either take and or we can take and , both will provide the same value of . Thus
THE DIFFERENCE TABLE


Years 
Production 




1990 – 91 
355 
73 
43 
20 
34 
1992 – 93 
428 
30 
23 
54 

1994 – 95 
458 
7 
31 


1996 – 97 
465 
38 



1998 – 99 
503 






148 
35 
74 
34 
Using the formula for Newton Interpolation, we have
For readjustment divide this result by 10, therefore,
Production (1997 – 98) = 47.542