Definition
As a rule, the phenomenon of interpolation is referred to as the process of selecting the data that can be located within a particular range of information (Groebner, Shannon, & Fry, 2014). The identified definition can be applied to a variety of domains, including business, technology, science, education, etc. Traditionally, interpolation occurs when two values in a particular sequence are known, and the need to identify another value within the range occurs.
Extrapolation, in its turn, implies that the data should be selected from the areas outside the selected range. In other words, the data that is being guessed should either exceed the largest number in the identified data set or lower than the lowest limit (Kharin, 2013). Therefore, the sequence of values determined prior to the statistical procedure is being extended so that data could be guessed correctly. Applying the definition provided for interpolation to explore the subject matter, one may assume that extrapolation takes place when two values within a data set are known, and there is the need to guess what data beyond the known limits also occurs in the data set in question.
Differences
At first glance, the concepts of inter- and extrapolation could seem the exact opposite of each other. Indeed, as the definition provided above shows quite explicitly, the primary difference between the two concepts concerns the range that the required number or item is taken from. Particularly, the scope of the choice (i.e., whether it is made within the identified range or beyond it) can be deemed as the crucial difference between the two notions.
Another characteristic feature of extrapolation that sets it aside from interpolation concerns the possibility of retrieving a negative answer. Although negative numbers may make sense for a number of statistical calculations and the related procedures, when applied to real objects, it may deliver rather pointless results (e.g., based on a specific set of data, one may calculate that one will eat minus one apple tomorrow, which is hardly possible). Naturally, the outcome can be tailored to the real-life scenarios so that the results could make sense (e.g., it can be assumed that the apple will be given to someone else as opposed to eating it), yet the difference between the two procedures is quite obvious (Bruce, 2015).
Examples
The identification of a mean in a sequence of three items can be interpreted as a common cause of interpolation and the simplest example thereof. For instance, if one said that they sent four e-mails to their friends three days ago and two e-mails a day ago, it can be interpolated that they sent three e-mails two days ago. Logically, it can also be extrapolated that one email will be sent tomorrow (Montgomery, 2014).
In a similar way, the concepts of inter- and extrapolation can be applied to a workplace setting. For example, if the team manager reports that the QA department failed to notice 67 defects two months ago and missed 53 defects last month, it can be interpolated that they omitted 60 defects a month ago. Consequently, it may also be extrapolated that they are likely to miss 46 defects next month (Yao, Lorenzelli, & Chen, 2013).
Although the phenomena of inter- and extrapolation can be deemed as rather basic, they serve as rather efficient tools in setting expectations. As a result, the team manager is likely to build a quality management strategy that will be viable in the environment that the staff members work in.
Reference List
Bruce, P. C. (2015). Introductory statistics and analytics: A resampling perspective. New York, NY: John Wiley & Sons.
Groebner, D. F., Shannon, P. W., & Fry, P. C. (2014). Business statistics (9th ed.). Upper Saddle River, NJ: Prentice Hall.
Kharin, Y. (2013). Robustness in statistical forecasting. New York, NY: Springer Science & Business Media.
Montgomery, D. (2014). E-Study guide for: Applied statistics and probability for engineers. New York, NY: 101 Textbook Reviews.
Yao, K., Lorenzelli, F., & Chen, C. E. (2013). Detection and estimation for communication and radar systems. Cambridge, UK: Cambridge University Press.