Extrapolation and Interpolation Study Notes

Extrapolation and Interpolation

Interpolation

• Definition: Interpolation is the process of making a prediction or estimate within the range of the data.

  • This method is considered safe and usually more reliable because it utilizes values that lie between known data points.

• Example: If temperature readings are known at 10 AM and 12 PM, one can interpolate to estimate the temperature at 11 AM.

Extrapolation

• Definition: Extrapolation is the process of making a prediction or estimate outside the range of the data.

  • This method is defined as less reliable because it involves making guesses based on information that lies beyond the available data.

• Example: If the last recorded data point is at 3 PM and an estimation is made for 5 PM, this act constitutes extrapolation.

Visual Examples

Interpolation Example Visualization

• The graph illustrates the following points:

  • A data point recorded at 10 AM with a value of 45.

  • A data point recorded at 12 PM with a value of 30.

  • A predicted temperature for 11 AM using the known values of 10 AM and 12 PM to estimate a value around 37.5 (an illustrative midpoint between 45 and 30).

Extrapolation Example Visualization

• Another graph shows:

  • Continuing from the last known data point at 3 PM with a value of 30, attempting to predict the value at 5 PM might involve a higher or lower estimation based on the trend, which is more uncertain due to lack of data.

  • This illustrates the potential deviation that could occur from the actual value.