Using existing data sets, a researcher can predict the value of future variables—this process is called extrapolation and it is extremely important in every systematic investigation. Instead of investing time and resources in simple research, you can project future variables based on primary and secondary data at your disposal. 

So, how do you go about this? To answer this question, let’s look at the different types and characteristics of extrapolation, plus how it contrasts with interpolation. 

What Is Extrapolation? 

Extrapolation is a statistical method of predicting the value or state of a variable based on its current state. In other words, the researcher studies the present condition of a variable and uses these insights to arrive at a realistic estimation for the future. 

Originally, extrapolation remained within the confines of statistics and quantitative research. However, as more fields of study infused statistical methods into their research process, extrapolation gained relevance in areas like Psychology and Sociology. In fact, it is useful in any subject that requires categorical data. 

Types of Extrapolation

While extrapolation passes as part of human instinct, it requires standardized processes during research. Based on these standards, we can identify 3 types of extrapolation—linear, conic, and polynomial. Let’s look at what they mean. 

1. Linear Extrapolation

Linear extrapolation is the process of estimating a value that is close to the existing data. To do this, the researcher plots out a linear equation on a graph and uses the sequence of the values to predict immediate future data points. You can draw a tangent line at the last point and extend this line beyond its limits.

Example of Linear Extrapolation

While calculating arithmetic progression, a researcher discovers that the recurring difference between existing values is 2. Against this knowledge, the researcher can accurately predict the value of future variables. 

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Uses of Linear Extrapolation

• It serves as a long-term estimate for data.
• Linear extrapolation can help estimate values that are either higher or lower than the values in the data sets.
• It can be used to fill gaps in data points for surveys.

Disadvantages of Linear Extrapolation

• Estimates given by linear extrapolation are never as good as using the equation from the line of the best fit method.

2. Conic Extrapolation

Comic extrapolation is a type of extrapolation that is done with a conic section paper template or on a computer. Here, the researcher depends on conic sections with known data to help them discover unknown data. To do this, the researcher creates a conic section which could be a circle, ellipse, parabola, or hyperbola using five data points near the end of the known variables. 

Read: What is Qualitative Data? + [Types, Examples]

3. Polynomial Extrapolation

Polynomial extrapolation is a statistical method that involves the use of polynomial shapes and functions to estimate the values on a graph. 

Advantages of Extrapolation 

1. Extrapolation is a simple method of data forecasting, and it doesn’t require lots of time or monetary resources.
2. In human resources, extrapolation can help you determine the appropriate compensation value for staff based on their current performance.
3. Extrapolation offers an effective means for businesses to project their future outcomes based on the current data at their disposal.
4. This forecasting method has low data requirements. This means you do not have to gather large data sets before you can predict future data points.

Disadvantages of Extrapolation 

1. Extrapolation is easily affected by significant fluctuations in the existing data sets.
2. Extrapolated values can be unreliable, especially when there are disparities in the existing data sets.
3. Extrapolation doesn’t account for qualitative values that can trigger changes in future values within the same observation.
4. It hardly accounts for causal factors in the observation.

Differences Between Extrapolation and Interpolation 

Interpolation and extrapolation are both forecasting methods, and it’s easy to mistake one for the other. In this section, we will discuss common differences and use cases for interpolation and extrapolation. 

• Definition 

Interpolation is a statistical method that allows researchers to estimate unknown values within a sequence of known data points. On the flip side, extrapolation is the process of predicting values for points outside the range of data. 

• Use Cases 

Interpolation is best for predicting unknown values, especially for geographical-related data points such as noise level, rain prediction, and the like. Meanwhile, extrapolation is best for predications like population growth based on its current size and growth rate. 

• Data Range

While extrapolation predicts data values outside a given data range, interpolation projects data points within the data range. In other words, extrapolation works outside the established range while interpolation works within two known values. 

Example of Extrapolation

If you spend twenty minutes from point A to point B, and you estimate that you’d spend the same time moving from point B back to point A, then you’ve applied extrapolation to your data sets. 

Read: Margin of error – Definition, Formula + Application

Example of Interpolation

Suppose the values in an arithmetic sequence are as follows: 2, 4, 6, ….., 10, 12. Using interpolation, you can determine the missing value in the sequence. 

Criticism and Limitations of Interpolation 

Like extrapolation, interpolation has several shortcomings.

For example, it cannot estimate above or below the maximum or minimum values in the observation. Other limitations of interpolation include the following: 

1. Someone, the data value resulting from interpolation isn’t very precise.
2. It could lead to a huge margin of error in the observation.
3. When applying interpolation to a large data set, you’d need to repeat several calculations.
4. It can demand lots of time and resources.

How to Gather Data for Extrapolation Using Formplus

Formplus allows you to collect data for quantitative research using surveys, polls and questionnaires. You can extrapolate these data sets to predict the behaviors and preferences of your target audience. 

Here’s a step-by-step guide on how to create a survey using Formplus. 

Step 1: Log into your Formplus account. You can create a free Formplus account here. 

Step 2: In the Formplus dashboard, click on the “create new form” button. This takes you to the form builder. Alternatively, you can choose the “templates” option, and select a sample survey for your needs. 

Step 3: In the form builder, you have access to numerous fields including text fields, rating fields, and advanced options like payment gateways and the digital signature field. Drag and drop the preferred form fields into the work area, to add them to your survey. 

Step 4: Edit form fields by clicking the “pencil” icon beside them. Save all your changes to access the builder’s customization option. 

Step 5: Use different customization options to change the look and feel of your survey. You can add background images, change the form font or customize the form layout. 

Step 6: Copy the form link and share it with respondents to collect data for extrapolation.