In a detailed comparison, we’ll look at the similarities and differences between interpolation vs extrapolation. The words “interpolation” and “extrapolation” may seem extremely technical, but they’re not that complex. Each term is employed somewhat differently, whether they’re being used generally or about math and data science. But we’ll see to it that you understand everything properly.

## Interpolation vs extrapolation: What do they mean?

Interpolation and extrapolation are used interchangeably to describe the process of replacing values in a sequence with new ones. In a broad sense, interpolation involves putting something between other items, whereas extrapolation entails drawing an inference about something unknown based on what is known.

Mathematically, interpolation is the technique of determining a random value within a sequence by using other data points. In contrast, extrapolation is the method for estimating a random number outside of a set by looking at the existing “curve.”

### What is extrapolation?

Extrapolation is making educated guesses about the future or some hypothetical situation based on data you currently have. You’re taking your best guess. Assume, for example, that your pay rises by an average of $200 each year. You may extrapolate that your compensation should be around $2,000 greater in 10 years.

### What is interpolation?

Interpolation enables you to predict within a data set; it’s a method of going beyond the data. It has a significant level of uncertainty. Let’s assume you track how many clients you acquire every day for a week: 200, 370, 120, 310, 150, 70, 90. According to that figure, you should be able to attract around ten customers per hour (1,310 customers/168 hours in a week). Let’s say you run your company around the clock to deal with those hourly customers. You’ll almost certainly receive no customers at night or on weekends, wasting time and money. (Note: a better approach to determine peak hours is via the Poisson Distribution).

### Cautions for interpolation and extrapolation uses

In general, you should extrapolate cautiously. For example, while a consistent salary coming in for a few months or years may be reasonable to assume, it’s probably not a good idea to expect the same firm will continue paying you 20 years down the road.

## What is the difference between extrapolation and prediction?

Interpolation is the process of estimating within the known data range. Extrapolation is the act of guessing the time of the gathered data. If we collected data every 15 seconds for 3 minutes, interpolation estimates would be estimates inside the 3-minute limit but not at precisely 15 seconds. Interpolation might produce figures after three minutes had elapsed since the start of monitoring.

### Main differences: Interpolation vs Extrapolation

- Interpolation results in more precise data or points than extrapolation.
- Interpolation is often simpler than extrapolation.
- Interpolation does not require extending previously established data points, whereas extrapolation does.
- Interpolation takes values from the start of one interval and interpolates them into the next. On the other hand, extrapolation takes values from a point outside the range and extrapolates them.
- Interpolation is less time-consuming than extrapolation.

### Prefixes

We must look at the prefixes “extra” and “inter,” which are both Latin, to distinguish between extrapolation and interpolation. The word “extraneous” refers to something outside or in addition to a group. “Inter” refers to anything in-between or among other things. Simply knowing these meanings (from their equivalent Latin roots) should be enough to tell the two methods apart.

### The setting

For both techniques, we make a few assumptions. We’ve established an independent variable and a dependent variable. We have a collection of pairs formed by sampling or collecting data. We also assume that we’ve developed a model for our data, even if it’s only for the least-squares line of best fit or some other type of curve that approximates our data. We have a relationship between the independent variable and the dependent variable represented by a function in this situation.

The objective is not simply to create a model for its sake but rather to apply our model for prediction. What will be the predicted value of the dependent variable when we have an independent variable? Extrapolation and interpolation are two methods for working with extrapolation and interpolation.

## Real-world examples: Interpolation vs Extrapolation

There are several real-world applications for interpolation and extrapolation, including:

### Mathematics

Many applications of mathematics allow for interpolation and extrapolation, which is why mathematicians must be conversant with both. In math, interpolation and extrapolation are frequently utilized to generate functions from graphs and locate missing values in data sets.

### Science

Interpolation and extrapolation are used in a wide variety of real-world applications in science. For example, you might use interpolation and extrapolation to build weather models or estimate unknown chemical concentration values. If you work in science, understanding interpolation and extrapolation will come in handy.

### Statistics

In statistics, interpolation and extrapolation are used in many ways. To collect, evaluate, and predict data in the field of statistics, interpolation and extrapolation are essential talents for statisticians. Statisticians frequently use extrapolation to assist them in determining unknown data from existing data. Statisticians may also utilize extrapolation to help them make predictions about future data based on past data, such as predicting population growth based on present-day demographic trends.

### Finance

Both interpolation and extrapolation have the same goal: to forecast values. Both prediction methods may be useful in finance since they are used to make predictions about financial data to assist businesses in creating budgets and planning for the future. You can analyze the stock market and make wise purchases using interpolation and extrapolation by financial analysts.

## Conclusion

Looking at the comparison interpolation vs extrapolation, the techniques of inferring data values from points to predict the graph’s nature are known as these terms. If you can form an equation that precisely points at a specific value, then you may get real values for data points. However, simple forms like a straight line or a constant curve are simple to solve. In the case of sophisticated patterns, such equations are difficult to discover. When interpolation becomes easier but extrapolation necessitates a lot of work, this concept of interpolation and extrapolation can be readily understood via a simple line.

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