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# Interpolation And Extrapolation In Statistics Pdf

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*Extrapolation is the process of taking data values at points x 1 , This is most commonly experienced when an incoming signal is sampled periodically and that data is used to approximate the next data point. For example, weather predictions take historic data and extrapolate a future weather pattern.*

*Question 1.*

Extrapolation is a useful statistical tool used to estimate values that go beyond a set of given data or observations. In this lesson, you will learn how to estimate or predict values using this tool. It could even be said that it helps predict the future! To help us remember what it means, we should think of the part of the word 'extra' as meaning 'more' data than what we originally had.

Extrapolation and interpolation are both used to estimate hypothetical values for a variable based on other observations. There are a variety of interpolation and extrapolation methods based on the overall trend that is observed in the data. These two methods have names that are very similar. We will examine the differences between them. For both methods, we assume a few things. We have identified an independent variable and a dependent variable.

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In the mathematical field of numerical analysis , interpolation is a type of estimation , a method of constructing new data points within the range of a discrete set of known data points. In engineering and science , one often has a number of data points, obtained by sampling or experimentation , which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate , i. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original.

Interpolation is the process of deriving a simple function from a set of discrete data points so that the function passes through all the given data points i. It is necessary because in science and engineering we often need to deal with discrete experimental data. Interpolation is also used to simplify complicated functions by sampling data points and interpolating them using a simpler function. Polynomials are commonly used for interpolation because they are easier to evaluate, differentiate, and integrate - known as polynomial interpolation. In Newton's method the interpolating function is written in Newton polynomial a.

Interpolation means to calculate a point or several points between two given points. For a given sequence of points, this means to estimate a curve that passes through every single point. Linear interpolation is the simplest interpolation method. Applying linear interpolation to a sequence of points results in a polygonal line where each straight line segment connects two consecutive points of the sequence. Therefore, every segment P; Q is interpolated independently as follows:.

*In this page you can download an Excel Add-in useful to linear, quadratic and cubical interpolation and extrapolation. The functions of this Add-in are very simple to use and they have context help, through a chm file. If you have an old release of Interpolation.*

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Abstract. —Interpolation is the process of calculating the unknown value from known given values whereas extrapolation is the process of calculating unknown values beyond the given data points.