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PSAT Prep: Help and Review18 chapters | 194 lessons

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Lesson Transcript

Instructor:
*Vanessa Botts*

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.

**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.

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.

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:

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.

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.

Extrapolation will not always be as easy as Mary's example. Sometimes, the data we work with will not have a linear relationship as shown on this graph.

As we can see on the graph above, there is no exact linear relationship between the data points. This means we will have to attempt to fit a linear model to the observed data. One method that could be used to fit the line is called linear regression. **Linear regression** is an analysis used to describe the data and also to forecast future values. After the line is found using linear regression, or a different method, the results may look something like this:

After we have found the line that fits, then we can extend that line in order to extrapolate, just as we did in Mary's example and as shown on the next graph.

With extrapolation, we are making predictions about future value, and it is important to note that the longer we extend the line, the more inaccurate our predictions will be. For instance, in Mary's example, our prediction of the plant's height on the fifth day is more accurate than the estimate for the tenth day.

As we have learned in this lesson, **extrapolation** is a useful statistical tool used to predict or estimate future values that go beyond those that have been observed or measured. We specifically focused on **linear extrapolation**. If there is an existing linear relationship among the data, all that needs to be done to extrapolate is to extend the graph line and estimate the desired values. If there is no linear relationship, then we must first find the best fit line using a method such as **linear regression**. One thing to remember is that the longer the line is extended from the original, the less accurate our predictions will be.

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PSAT Prep: Help and Review18 chapters | 194 lessons

- Understanding Bar Graphs and Pie Charts 9:36
- How to Calculate Mean, Median, Mode & Range 8:30
- Finding and Classifying Geometric Sequences 9:17
- Probability of Independent and Dependent Events 12:06
- Probability of Simple, Compound and Complementary Events 6:55
- Probability of Independent Events: The 'At Least One' Rule 5:27
- Either/Or Probability: Overlapping and Non-Overlapping Events 7:05
- How to Calculate the Probability of Combinations 11:00
- How to Calculate the Probability of Permutations 10:06
- Math Combinations: Formula and Example Problems 7:14
- What Is a Factorial? 5:24
- Factorial Practice Problems 6:04
- Extrapolation in Statistics: Definition, Formula & Example 4:08
- Mean: Definition & Sample Problems
- Minimum Values: Definition & Concept 4:50
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