Interpolation Vs. Extrapolation: What’s The Difference?

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Interpolation Vs. Extrapolation: Understanding the Key Differences

Statistics can often seem daunting, but the core concepts are well within reach. Understanding the fundamentals of statistics empowers you to critically assess information and avoid being misled.

While interpolation and extrapolation have meanings beyond the realm of mathematics, they are frequently confused in statistical contexts. The key to distinguishing them lies in their prefixes.

Interpolation refers to predicting values that lie within a given data set (indicated by the prefix inter-), whereas extrapolation involves predicting values that fall outside the data set (indicated by the prefix extra-).

Key Takeaways:

Interpolation	Extrapolation
This is a type of prediction for values that exist between your known data points.	This is a type of prediction for values outside your known data points.
Derived from the Latin interpolatus, meaning to alter or refurbish.	Derived from the Latin polare, meaning to polish, combined with extra- which means outside or beyond.
The term ‘interpolate’ was first used in English in 1612.	The term ‘extrapolate’ was first recorded in 1874.
Common forms of mathematical interpolation include piecewise, constant, linear, polynomial, mimetic, and spline.	Common types of mathematical extrapolation include linear, polynomial, conic, French curve, and geometric extrapolation with error prediction.
Interpolation is generally accurate within known data ranges.	Extrapolation tends to be less accurate as it ventures further from known data points.

What Is Interpolation?

Interpolation is the process of estimating a value within the boundaries of a data set. This value is hypothetical and represents a potential data point that lies between recorded values on a graph.

There are various types of interpolation techniques:

Piecewise constant interpolation. Known as nearest neighbor interpolation, it assigns the nearest known data point value to estimate the next value.
Linear interpolation. This widely recognized method connects two data points with a straight line, enabling the identification of intermediate values.
Polynomial interpolation. This method employs higher-degree polynomials to create a curved line that better fits the data.
Spline interpolation. Similar to polynomial interpolation, but it utilizes lower-degree polynomials to create smoother curves known as splines.
Mimetic interpolation. Often used with vectors, this method is more abstract and relies on geometric projections.

Though commonly associated with mathematics, the term “interpolate” can also imply inserting additional information, often with negative connotations when it refers to altering original texts or documents. The word originates from the Latin interpolare, which means to alter or refurbish, with a first known use in English dating back to 1612.

What Is Extrapolation?

Extrapolation is a method of estimation that predicts values beyond the existing data points. Instead of estimating values between known data points, extrapolation extends the trend established by the data into the future.

There are several extrapolation methods:

Linear extrapolation. This method mirrors linear interpolation but extends beyond the existing data points using the same equation.
Polynomial extrapolation. Similar to polynomial interpolation, this technique fits a polynomial curve to the data and extends it beyond the known values.
Conic extrapolation. Utilizing the final five data points, this method creates a conic section that may or may not loop back to meet itself, depending on its shape.
French curve extrapolation. This technique is effective for data exhibiting exponential trends and is best suited for data with accelerating or decelerating characteristics.
Geometric extrapolation with error prediction. This method requires a substantial amount of known values, typically at least three data points.

The term “extrapolate” is often used in both mathematical and conversational contexts to refer to predictions based on known data, but it generally becomes less accurate as it moves further from the known data points. The term originates from the Latin polare, meaning to polish, with its first use recorded in 1874.

Interpolation vs. Extrapolation FAQs

What is the root word of interpolation?

The root word for interpolation comes from the Latin word interpolate, which means to refurbish or alter. Interpolire is derived from polire, meaning “to polish,” and the prefix inter- signifies “between, among, or in the midst.”
What’s a real-world example of extrapolation?

A real-world example of extrapolation is modeling the expected spread of a disease. Many predictions regarding the spread of COVID-19 were forms of extrapolation, as well as those for other health crises, including HIV and various influenza outbreaks.
Can extrapolation be used to predict the value of a point?

Extrapolation can indeed be used to predict the value of a specific point. However, greater specificity in predictions typically results in decreased accuracy, especially if the point lies far outside known data.

None of the methods listed for extrapolation inherently generate points, but a specific point can be identified from the resulting extrapolated line.
What’s the difference between linear interpolation and linear extrapolation?

The key difference is that linear interpolation predicts values between known data points while linear extrapolation predicts values outside these points.

Although both methods utilize the same equation and operational concept, interpolation is generally more accurate than extrapolation due to its reliance on established data.

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Author

Di Doherty

Di has been a writer for more than half her life. Most of her writing so far has been fiction, and she’s gotten short stories published in online magazines Kzine and Silver Blade, as well as a flash fiction piece in the Bookends review. Di graduated from Mary Baldwin College (now University) with a degree in Psychology and Sociology.

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