Interpolation and extrapolation are two methods of finding different values which come under a sequence of a straight line or in the same pattern of a curve. Such values can only be found if two points associated with the line or curve are known. This further helps in forming an equation that can give the exact value of the curve.
Interpolation vs Extrapolation
The main difference between interpolation and extrapolation is that interpolation gives more accurate values compared to extrapolation. Interpolation requires picking values that are actually between the data points received from research or study. Extrapolation requires picking values that are beyond the data points one has received through the experiment or research.
Interpolation involves finding one value based on another value, and these two values lie in between some of the data points one already knows are accurate. These points may be part of a straight line with an equation or a curve with the constant curving. One can find values more easily and accurately through it.
Extrapolation involves finding one value based on another value and these value lie beyond some of the data points that one already knows is accurate. These points may be part of a straight line with an equation or a curve with the constant curving. It could sometimes be difficult to find values in extrapolation.
Comparison Table Between Interpolation and Extrapolation
| Parameters of Comparison | Interpolation | Extrapolation |
| Extension | It does not require an extension of the pattern. | It requires an extension of the pattern. |
| Finding data points | Data points are found within the range. | Data points are not found within the range. |
| Convenience | It is more convenient to find data points here. | It is less convenient to find data points here comparatively. |
| Accuracy | The data points or simple points found here are more accurate and precise compared to extrapolation. | There is more chance of finding inaccurate data points in this process compared to interpolation. |
| Easy | One can easily find data points in this process. | One cannot easily find data points in this process. |
What is Interpolation?
Interpolation is the process of finding values that fall under a particular range of values. Interpolation helps to find data that is part of a data range. During the process, it should be made sure that in an area where the values can fluctuate vigorously, more sample spaces are taken so that a more accurate value can be found.
An example of this process could be finding the weather of a particular region at a particular point in time. It is impossible to find whether phenomenon at every point of the location. Hence only a few points of a particular location are taken as a reference point so that the rest are determined based on the constant pattern with the help of interpolation.
Hence, the process makes it easier to find points around a large surface area. An easier way to understand interpolation is by taking an example of a straight line. When two points are connected to each other on a plane surface, an equation can be found for the line based on the two points of reference.
Further, one can draw a line to connect these two points. There are various other points that are connected on the ways of connecting these two points, and these can be taken as the points that are found using the interpolation process. This is because these lie in between the two known points and hence have an accurate value with reference to the line.
What is Extrapolation?
Extrapolation can be a little complicated than compared to of interpolation. Similar, to interpolation it requires one to find points, but this time the points do not lie in between the data points we already have. During this process, the data lies in that part of the curve, line, or pattern which is beyond the pattern we have made.
Hence the pattern needs to further extend. If the extension of the graph pattern is not possible, one has to find an estimated point according to the pattern. There are a lot of possibilities that the points are not accurate or exact.
This point lies beyond the surface or area that we are known about. One example of this is a plane connecting two points. When we join them with the help of a line, the line incorporates an infinite number of points in it.
However, the point that lies outside these two points connecting each other requires extrapolation. These points can be easily located if the line is further extended, but this is not always possible, similar to the case of finding whether points of a location.
Main Differences Between Interpolation and Extrapolation
- Interpolation gives more accurate data or points compared to extrapolation.
- Interpolation can be a little easier than extrapolation.
- Interpolation does not require one to extend the already existing data points, where extrapolation requires elaboration of the pattern, curve, or line.
- Interpolation has values within the range, whereas extrapolation does not.
- Interpolation requires less time than extrapolation.
Conclusion
Both interpolation and extrapolation are the processes of finding data values within points so as to predict the nature of the graph. One can find exact values of data points if they are able to frame an equation that exactly points at a particular value. However, such equations are easy to make in the case of simple patterns like a straight line or a constant curve. In the case of complicated patterns, such equations are hard to find. That is when interpolation becomes easier, but extrapolation requires a lot of effort. Hence the concept of interpolation and extrapolation can be easily understood using a simple line and, in the long run, help to understand complicated graphs as well.
References
- https://psycnet.apa.org/record/2001-06109-008
- https://link.springer.com/article/10.1007/BF01396314