# What is Extrapolation?

## Extrapolation

Extrapolation is a statistical method that involves estimating unknown values by extending or projecting from the known values. In other words, it’s a technique used to predict or forecast beyond the observed range of data.

The premise behind extrapolation is that the current trend or pattern observed in the data will continue into the future or extend to other data points. This is commonly used in many fields, including finance, economics, physics, engineering, and more.

However, extrapolation must be used with caution. Its accuracy can be highly variable because it assumes that the current trend or pattern will continue unchanged. In many cases, this is not a safe assumption, especially when extrapolating far beyond the range of the observed data. Any unexpected changes or events that are not reflected in the existing data can significantly impact the results.

It’s also worth noting that extrapolation is different from interpolation, which is a method used to estimate values within the range of known data. Extrapolation extends beyond the known data, while interpolation stays within it.

## Example of Extrapolation

Suppose a company has been growing its sales by 10% each year for the past five years. The sales for the most recent year (Year 5) were \$110,000.

If the company wants to forecast its sales for the next year (Year 6) and assumes the same growth rate of 10%, they can use extrapolation.

Here’s how they’d do it:

\$110,000 (Year 5 sales) * 10% (growth rate) = \$11,000 (increase)

\$110,000 (Year 5 sales) + \$11,000 (increase) = \$121,000

So, based on the extrapolation, the company would expect its Year 6 sales to be around \$121,000.

However, it’s important to remember that this is an estimate based on the assumption that the 10% growth rate continues. In reality, many factors could cause the actual sales to be higher or lower, such as changes in the market, competition, or the overall economy. This is why caution must be exercised when using extrapolation, especially for longer-term forecasts or those based on a small amount of data.