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What is interpolation and extrapolation?
some of us tend to use the word extrapolate a lot. When we say it in common speech, we generally mean that we are pulling a piece of information from a larger set of data. however, extrapolation has an importance statistical meaning as does its counterpart interpolation. In this video we're going to explore the actual definition behind these terms and the important difference between the two mathematically. Buckle up, it's time to get some nerd on. The word interpolate means estimating or calculating a point that is in-between two known values. The important key here is that the point we are concerned about is in between two known values. When we run a flow test, as an example, we gather the pressure that is at a no flow condition, and then we also grab a lower pressure when we flow water. When we estimate our pressure at any flow in between these two values, this would be an interpolation. It's an interpolation because our estimated point is in between two known values. The word interpolation comes from Latin and has a prefix inter- that means among or between. We can remember that interpolation means that we're grabbing a point in between two known values. This is different from extrapolating. The prefix extra- also comes from Latin and it means outside. When we extrapolate information, we are estimating a value that is outside of our known conditions. We are estimating an area that is not known or tested. In common language we often say that we extrapolate something from data as in we are just taking it from data, but the actual defined meaning of extrapolate is when we are predicting some value that is outside of our known range. We are taking the known relationship that we have from the data that we have gathered, and extending that relationship outside of the boundaries of what we actually know. When we create a chart to show the hydraulic relationship between flow and pressure for our system, we are creating a model so that we can try and predict how much water is available on that supply. This is a model and not an absolute certainty. These values can fluctuate daily and seasonally, which we'll talk about later, and the Hazen-Williams formula is the method in which we model our hydraulic relationship. Each point that we gather during a flow test is just a single snapshot in time period we are not monitoring the fluctuation and variation that happens through the entire water supply. We are using this information to model and then estimate how much water is available in the water supply. Let's say we have a flow test result that is 90 PS I static and 40PSI residual at 1000 GPM. We then model the relationship using the hazen Williams formula and chart that on a graph. If we estimate the pressure for any flow between zero and 1000 GPM, then the pressure that we estimate would be considered an interpolation. If we pull a value that is greater than 1000 GPM, this would be outside of our two known points, and would be considered extrapolation. Of these two methods, interpolation is preferred. This is because we have a greater likelihood of getting a valid estimate. When we extrapolate, we are making an assumption that our trend continues for flow rates that are outside of the range that we tested. This very well could be the case, but we don't have as much certainty for this range as we do for our known values. Some consultants and insurance providers require that the flow rate achieved during a flow test is greater than the demand of the suppression system itself. In essence this requirement is pushing out the range and allowing us to interpolate instead of extrapolate the water supply. We know, because we have tested it, that our water supply can achieve the flow and pressure that we are needing for our system. The interpolation carries with a confidence that the system can handle the flow rate, and the entire system isn't based on just an assumption that the water supply will continue to perform beyond our tested range with the same relationship that we expect. What is interpolation and extrapolation? interpolation is estimating a value that's in between two known quantities, while extrapolation is estimating a value that is outside of a known range. We are generally less confident in the values that we extrapolate when compared to values that we interpolate. When do we extrapolate values? when we look to predict fireflow, which will cover in more detail later. In the next video we'll explore why it's important to achieve a high flow rate during a flow test Which relates to our interpolation and extrapolation mindset. I'm Joe Meyer, this is MeyerFire University.
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