Extrapolation is the process of obtaining values from a graph or a table that are extend beyond the given data. The trend of the data is extended beyond the last point given, and based on this extended trend an estimate of the value is made.Interpolation is the process of obtaining values from a graph or a table that are located between two major points or values known. A ratio process is usually employed for interpolation.
One of the best means of extrapolation and interpolation is to plot the given data on a graph and develop a smooth curve to fit all the points plotted. The smooth curve to fit the points plotted can be drawn by using personal judgement, which may be aided by use of stencils of curves of different shapes. Also mathematical techniques are available to develop equations of curves that best fit the given data. The advantage of using these mathematically derived curves is that it is possible to clearly define how well the curve fits the given data. further, the equations of the curve enables to understand relationships between different variables better and to use this understanding for further analysis. Finally, equations are more handy to use then graph. However, the graph method is easier to understand and use for people not familiar with mathematical techniques.