Extrapolation and interpolation is used for assessment of hypothetical values of a variable on the basis of third-party observations. There is a set of ways of their use which are based on the general trend of observation of data. Despite similarity in names, between them there is a big difference.
Prefixes
To define a difference between extrapolation and interpolation, we have to look at prefixes "extra" and Inter. The prefix "extra" literally means — "beyond limits" or in "addition to". The prefix means Inter - "between" or "among". Knowing it it is possible to distinguish easily methods among themselves.
Use of methods
For both methods several entry conditions are supposed. At first it is necessary to define what will be independent, and that a dependent variable for our case. By means of data collection there is a dual number of their values. It is also necessary to formulate model for basic data. All this can be written down in the table for the best presentation. Then the schedule of dependence is under construction. They often represents any curve which approximately characterizes data. Anyway, there is a function which connects an independent variable with dependent. The purpose of these transformations is not only the model. As a rule, it is used for forecasting. In particular, it is necessary to consider an independent variable which will be the predicted value of the dependent variable corresponding to it. The output value of our independent variable will show whether extrapolation or interpolation was correctly used.
Interpolation
It is possible to use the received function to predict value of a dependent variable for independent which is implicitly expressed. In this case the interpolation method is used. Let's assume that the value x between 0 and 10 is used for function creation: at = 2x + 5; We can use this function for the best assessment of the size at corresponding to value x =6. For this purpose we will just substitute this value in the initial equation. It is simple to see result: at = 2 (6) + 5 = 17;
Extrapolation
It is possible to use initial function to predict value of a dependent variable for an independent variable which is out of the range of values. In this case extrapolation is used. Let, as well as before the value x is between 0 and 10 and there is a function: at = 2x + 5; To estimate value y with the help x =20, it is necessary to substitute this value in our equation: at = 2 (20) + 5 = 45; If the value x is not included into the range of permissible values, then the method of check is called extrapolation.
Pay attention
From two methods, interpolation is preferable. It so because at its use there is a high probability of receiving reliable assessment. When we use extrapolation, the assumption becomes that our trend will remain for values x and outside the range which was set initially. It can not always be so and therefore it is necessary to be very careful when using a method of extrapolation.