Chapter 2 Excel Fundamentals Linear Interpolation Chapter 2 Excel Fundamentals Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1

Population Example The population data of a town is given in the table We maywant to estimate the population in any year: 1995, 1983, etc. Engineering Computation: An Introduction Using MATLAB and Excel 2

Linear Interpolation With linear interpolation, we assume that our data varies linearly between data points: Engineering Computation: An Introduction Using MATLAB and Excel 3

Formula for Linear Interpolation Point x falls between x1 and x2. The y-values corresponding to x1 and x2 are given (y1 and y2, respectively). Find the y value corresponding to x. x1 x2 y2 y1 x y Engineering Computation: An Introduction Using MATLAB and Excel 4

Formula for Linear Interpolation Engineering Computation: An Introduction Using MATLAB and Excel 5

Population Example y2 = 4086 y y1 = 3012 x = x1 = 1950 x2 = 1960 1956 Engineering Computation: An Introduction Using MATLAB and Excel 6

Linear Interpolation Description (increase in x) * slope + starting y value (y1) increase in x = x – x1 slope = (y2 – y1)/(x2 – x1) If population = 7000 (y1) in 2000 (x1) 8000 (y2) in 2010 (x2) Population in 2008 = (2008 – 2000)*(8000 – 7000)/(2010 - 2000) +7000 8*(1000/10) + 7000 8*100 + 7000 7800 Engineering Computation: An Introduction Using MATLAB and Excel 7