Extrapolation in Statistics: Definition, Formula & Example

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  • 0:02 Definition and Use of…
  • 0:36 Example 1
  • 1:14 Example 2
  • 2:28 Example 3
  • 3:13 Caution with Extrapolation
  • 3:30 Lesson Summary
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Lesson Transcript
Vanessa Botts
Expert Contributor
Will Welch

Will has a doctorate in chemistry from the University of Wyoming and has experience in a broad selection of chemical disciplines and college-level teaching.

Extrapolation is a useful statistical tool used to estimate values that go beyond a set of given data or observations. In this lesson, you will learn how to estimate or predict values using this tool.

Definition and Use of Extrapolation

Extrapolation is the process of finding a value outside a data set. It could even be said that it helps predict the future! To help us remember what it means, we should think of the part of the word 'extra' as meaning 'more' data than what we originally had. This tool is not only useful in statistics but also useful in science, business, and anytime there is a need to predict values in the future beyond the range we have measured. There are several methods for extrapolation, but in this lesson we will focus on linear extrapolation, which is using a linear equation to find a value outside a data set.

Example 1

Let's try a basic extrapolation by finding values in a numerical sequence. When using extrapolation, we look for the relationship between the given values. So, let's look at the following numerical sequence. What is the relationship between the values in the sequence?

2,4,6,8, ?

Pretty easy, right? The numbers in the sequence are increasing by 2. Now, by using extrapolation we can predict the fifth term in each sequence. The fifth term of the sequence is 10. However, extrapolation goes beyond estimating future values in numerical sequences, as we will see in the next example.

Example 2

My friend Mary planted a bean plant, and she has been measuring and keeping track of its growth for the past four days. Based on her observations, she wants to estimate how tall her plant will be on the 5th day.

Her chart of observations looks like this:

data table

Based on Mary's chart, it is not too difficult to predict that the plant will be 10 mm tall on the fifth day. But, what if Mary wanted to predict the plant's height on the tenth day? In that case, extrapolating from a graph would come in handy. To illustrate this, let's plot her observations on a graph. When we plot the data, we realize there is a linear relationship between the number of days and the growth of the plant.

line graph 1

On the graph, we can also see that there are data points for four days of observation. However, Mary wants to know how tall her plant will be on the tenth day. This would not be too difficult to do using extrapolation. We just need to draw a line through the data points and then extend the line past the tenth day mark.

If we take a look at the next graph, we can see the extended line and with that, we can estimate that the height of the plant would be 20 mm on the tenth day.

line graph 2

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Additional Activities

Research Activity on World Population Projections

This activity requires a bit of light internet research, specifically to obtain world population projections, which are available in abundance from many sources.

It is meant to expose students to real extrapolated data and think about what it means.

1. Obtain some data.

  • First, search "world population projections" and browse images, specifically looking at graphs.
  • Examine the different types of plots. Find some that show lines indicating population as a function of time.
  • Select a few graphs that are easy to understand, representing different populations, for example the world, a continent and a country.

2. What's in the data?

  • Describe what each axis represents and what the direction of the trendline says.
  • Which data is observed and which data is extrapolated?
  • Is the data linear over any region? Is it not linear over any region?

3. Nonlinear projections.

  • Some graphs are bound to have nonlinear projections. Discuss the reasons that a population may be projected to change in a nonlinear way.
  • What kinds of factors may scientists consider to make a population projection?

Guidelines and Possible Answers to Questions

1. There will be plenty of usable data to chose from.

  • There are a lot of projections for this and most of the data is presented in a simple line plot of "population vs. time," which is what you want. It is interesting to look at places with different slopes and projections and talk about where the differences might have come from.

2. The data will vary depending on what students choose.

  • The y-axis may have populations expressed in millions, billions or percent change. The x-axis should be time.
  • Data from the past should be observed and data for future populations is extrapolated.
  • Most population data of this type will have both linear and non-linear regions.

3. Nonlinearity - population growth is never truly linear, but usually has a very linear phase and then tapers off.

  • Populations can't grow forever for a lot of reasons. People run out of room and resources, etc.

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