There are two ways in which you can obtain results from a completed graph. One is by interpolation and the other is by extrapolation. What is the difference between these two terms and which one do you believe may lead to erroneous conclusions and why?
My answer:
Interpolation is estimating the value of a quantity from known values on either side of it (the neighboring data). This is a mathematical method of creating missing data. Extrapolation is an explanation of unknown values by extending the curve from known values, that is into the future by assuming the known values will continue to behave as they have in the past.
Is this correct so far and which one leads to erroneous conclusions?
THanks
correct. The extrapolation can lead to serious error. Why? It is safe to be bounded on each side, but if one is extroplating into the unknown from one point...
Yes, you are correct so far. Interpolation involves estimating values within the range of known data points, whereas extrapolation involves extending the curve beyond the known data points to estimate values outside the range of known data.
Extrapolation is more likely to lead to erroneous conclusions compared to interpolation. This is because when extrapolating, you are assuming that the trend or pattern observed in the known data will continue indefinitely. However, this assumption may not always hold true, especially when the extrapolation is done far beyond the range of the known data.
The further you extrapolate, the greater the potential for error because the assumptions about the data's behavior become less reliable. Factors such as outliers, changes in underlying conditions, or unforeseen events can significantly affect the future data points, making the extrapolation inaccurate.
Therefore, it is generally recommended to be cautious when using extrapolation, especially if it involves projecting far into the future or outside the range of the known data. It is often considered more reliable to rely on interpolation within the known data range to avoid erroneous conclusions.