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### Interpolation and Extrapolation

```
Date: 08/10/99 at 21:40:18
From: Ramon Santiago
Subject: Interpolation

I can't remember the proper way of solving interpolation problems.
It's been a long time since I finished my degree, and very few times
that I've needed to interpolate something.

I want to find the step-by-step procedure for finding the missing
values of X and Y based on existing given values as shown below:

26 -> 1800
28 -> X
32 -> 2400
44 -> Y

I hope somebody there in your group can help me.

Thanks
Ramon
```

```
Date: 08/11/99 at 03:04:47
From: Doctor Floor
Subject: Re: Interpolation

Dear Ramon,

Thanks for writing to Ask Dr. Math.

Let me first explain a little bit about the term "interpolation."

"Interpolation" means that you have to calculate a value between
("inter" is Latin for between) two given values.

There are several types of interpolation, but in this case I suppose
you want to use "linear interpolation," which is based on the fact
that the values are increasing or decreasing linearly.

"Extrapolation" is the term you should use when you have to calculate
a value before or beyond the given values ("extra" is Latin for
outside). That's what you should do to find Y.

26 -> 1800
28 -> X
32 -> 2400
44 -> Y

We see that if the left value increases from 26 to 32, which is +6,
then the right value increases from 1800 to 2400, which is +600. If we
assume linear behavior, then we must conclude that if the left value
increases by 1, the right increases by 100.

And we find:

Interpolating: When the left value increases from 26 to 28, which is
+2, the right value increases by 200. So X = 1800+200 = 2000.

Extrapolating: When the left value increases from 32 to 44, which is
+12, the right value increases by 1200. So Y = 2400+1200 = 3600.

If you need more help, just write us back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
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High School Definitions
High School Sequences, Series

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The text passage contains a question about interpolation and extrapolation, and it provides a detailed answer with step-by-step calculations for finding the missing values of X and Y.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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### Interpolation and Extrapolation

```
Date: 08/10/99 at 21:40:18
From: Ramon Santiago
Subject: Interpolation

I can't remember the proper way of solving interpolation problems.
It's been a long time since I finished my degree, and very few times
that I've needed to interpolate something.

I want to find the step-by-step procedure for finding the missing
values of X and Y based on existing given values as shown below:

26 -> 1800
28 -> X
32 -> 2400
44 -> Y

I hope somebody there in your group can help me.

Thanks
Ramon
```

```
Date: 08/11/99 at 03:04:47
From: Doctor Floor
Subject: Re: Interpolation

Dear Ramon,

Thanks for writing to Ask Dr. Math.

Let me first explain a little bit about the term "interpolation."

"Interpolation" means that you have to calculate a value between
("inter" is Latin for between) two given values.

There are several types of interpolation, but in this case I suppose
you want to use "linear interpolation," which is based on the fact
that the values are increasing or decreasing linearly.

"Extrapolation" is the term you should use when you have to calculate
a value before or beyond the given values ("extra" is Latin for
outside). That's what you should do to find Y.

26 -> 1800
28 -> X
32 -> 2400
44 -> Y

We see that if the left value increases from 26 to 32, which is +6,
then the right value increases from 1800 to 2400, which is +600. If we
assume linear behavior, then we must conclude that if the left value
increases by 1, the right increases by 100.

And we find:

Interpolating: When the left value increases from 26 to 28, which is
+2, the right value increases by 200. So X = 1800+200 = 2000.

Extrapolating: When the left value increases from 32 to 44, which is
+12, the right value increases by 1200. So Y = 2400+1200 = 3600.

If you need more help, just write us back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Definitions
High School Sequences, Series

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search
user
The text passage contains a question about interpolation and extrapolation, and it provides a detailed answer with step-by-step calculations for finding the missing values of X and Y.

TYPE: SINGLE_QUESTION_WITH_ANSWER