# Interpolation vs. extrapolation: What's the difference?

By Indeed Editorial Team

Published 14 November 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Mathematical techniques such as interpolation and extrapolation are useful for making sense of data and using it to predict outcomes. These are some of the most common prediction techniques, and they have their own set of sub-methods that professionals use to conduct them. If you're a professional who works with data, such as a mathematician, engineer or statistician, you may benefit from learning more about these concepts. In this article, we explain the differences between interpolation vs. extrapolation, discuss how they work and when to use each prediction method and provide some examples of these techniques.

## What is interpolation vs. extrapolation?

When comparing interpolation vs. extrapolation, it's important to understand that they're both mathematical prediction techniques but with key differences. While they have similar sounding names, they have unique functions, and professionals apply them in different situations. Extrapolation is good for predicting values that are outside of a data set, using known values to predict unknown ones. In contrast, interpolation is useful for predicting values that exist inside a data set. Each method is useful in different scenarios, but interpolation typically produces more reliable results.

When conducting either of them, there are various methods available to use, like polynomial and linear prediction methods. Typically, professionals draw curves or lines on graphs or use known functions to conduct interpolation and extrapolation. These techniques have many applications in industries relating to science, finance, statistics and mathematics, as they help organisations understand future trends.

Related: Careers in maths and tips to get mathematics degree jobs

## How does interpolation work?

Professionals use this method to estimate hypothetical values that a data set contains. This enables them to extract functions from these values, which helps with identifying new points in the data set. The following are some of the most common interpolation methods:

Polynomial interpolation: This interpolation method comprises the use of polynomial functions to predict values inside gaps in data sets on graphs.

Linear interpolation: This is a simple interpolation method that involves drawing straight lines between different points on graphs to figure out what the other values in the data set are.

Spline interpolation: Spline interpolation is a method that involves using piecewise functions to guess the values within gaps in data sets, and this method sometimes produces more reliable results than polynomial interpolation.

To illustrate, imagine a line on a graph connecting two data points with a gap between them. Interpolation can enable you to deduce which points constitute the missing portion, as you can draw a line or curve between the data points and visualise the missing values. There's a greater chance that the value you estimate is correct when using interpolation over extrapolation, which is why many prefer this method.

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## How does extrapolation work?

This method enables professionals to estimate hypothetical values that don't exist within a set of data points. The following are some popular extrapolation methods:

Polynomial extrapolation: Like polynomial interpolation, this method relies on the use of polynomial functions and shapes to predict values on graphs.

Linear extrapolation: This method involves using linear functions and drawing lines on graphs to estimate values that fall outside of a data set.

Conic extrapolation: To conduct conic extrapolation, professionals use conic sections with existing data to predict unknown data.

Fast Fourier transform extrapolation: This method converts data from time domains to frequency domains, the results of which you can extrapolate by adding and subtracting harmonics.

You illustrate extrapolation by applying data to a graph. If this graph has a function with various plotted data points, you can use extrapolation to predict unknown values. You can extrapolate the function if you draw a curve or line between the points or use a function like hyperbolas or parabolas. Extrapolation can also mean assuming something based on the information you have access to, especially in fields outside of mathematics. Many consider extrapolation to be riskier than interpolation, so ensure to apply it correctly to avoid inaccuracies.

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## When to use interpolation vs. extrapolation

These similar-sounding terms have key differences that are important to be aware of, as this can help you use the most appropriate method for each situation. Generally, interpolation produces more reliable results than extrapolation, which is why professionals tend to use it when the accuracy of predictions is paramount. Although, in a situation where you're predicting a value that falls outside of a data set and using known values to predict unknown values, always use extrapolation. When you want to predict a value that exists within a set of data points, use interpolation.

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## Real-world examples and career applications of interpolation and extrapolation

There are many real-world examples and career applications of interpolation and extrapolation, which include the following:

### Mathematics

The field of mathematics has many uses for interpolation and extrapolation, and it's important for mathematicians to understand both types of predictions. In mathematics, professionals typically use interpolation and extrapolation to derive functions from graphs and find unknown values in data sets. Mathematicians can apply these skills in a range of careers, including education, engineering, finance, information technology, insurance and the civil service.

Related: How to become a mathematical engineer: step-by-step guide

### Science

Interpolation and extrapolation have a variety of real-world applications in the field of science. For example, you could use interpolation and extrapolation to create models to forecast the weather or predict unknown chemical concentration values. Communications professionals can also use them to predict the original data of signals after they experience alteration during transmissions, allowing them to reconstruct original audio files. The field of science often involves analysing data, making an understanding of interpolation and extrapolation very useful if you work in this career field.

Related: 10 examples of careers in STEM (with definitions and types)

### Statistics

Statistical professionals also find many useful applications for these techniques. Because the role of a statistician involves collecting and analysing data and making predictions, they often require a good understanding of interpolation and extrapolation. This is because they can help statisticians figure out unknown information using data they have access to, which, in turn, assists them in making assumptions about the future. They may also use the techniques to predict future trends, such as population growth, as statisticians can look at historical growth data to forecast future outcomes.

Related: 7 popular mathematics degree jobs (with examples and salaries)

### Finance

Financial professionals commonly apply interpolation and extrapolation, as the ability to predict values is highly valuable in this field. For example, if a financial analyst wanted to make predictions about financial data to serve their employer or clients, they could do so using these techniques. This helps them find value for their clients and assists businesses in planning for the future. Many investors also use the techniques to predict the movements of stocks on the stock market, which helps them make intelligent investments.

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### Education

Teachers of various disciplines use interpolation and extrapolation when teaching students about these concepts. They do this in finance, economics, statistics and other science, technology, engineering and math (STEM) fields. When doing lectures and seminars, teachers and professors within these disciplines may teach their students various methods of interpolation and extrapolation, giving them useful skills to apply in their careers. They may use different methods depending on the subject.

### Aerospace engineering

Engineers use these mathematical techniques to launch rockets into space. They use formulas representing each of the parameters of rockets, such as their speed, temperature and acceleration, as these are the known variables they measure at regular intervals. If something unexpected happens or ground control loses communication with the craft, they can interpolate missing information using existing data. For example, if the rocket loses signal for a brief time, engineers and scientists on the ground can interpolate information to determine the readings of functions during the offline period.

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