CHEM%20140L%20Session%2007

CHEM%20140L%20Session%2007 - Session 07 Data Analysis in...

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7-1 Session 07 Data Analysis in Mathcad Topics In this session the following spreadsheet concepts will be explored: 1. Statistical Functions in Mathcad 2. Error Bars 3. Interpolation Linear Interpolation Cubic Spline Interpolation 4. Curve Fitting Simple Linear Regression Generalized Linear Regression Specialized Regression Equations Quality of Fit
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CHEM 140L Session 7 - Data Analysis in Mathcad 7-2 Statistical Functions in Mathcad Students are encouraged to review the section “Basic Statistics in Science” found in Session 03 of this manual. Mathcad has several built-in functions that are commonly used in statistical calculations. Some of the more common statistical functions used in science are given below. Notice that Mathcad uses lowercase s and v for population functions ( σ , σ 2 ), and upper-case S and V for sample functions ( s , s 2 ). Function Calculates mean(A, B, ÿ ) The mean of all the elements in arrays A , B , ÿ stdev(A, B, ÿ ) The population standard deviation of all the elements in arrays A , B , ÿ var(A, B, ÿ ) The population variance of all the elements in arrays A , B , ÿ Stdev(A, B, ÿ ) The sample standard deviation of all the elements in arrays A , B , ÿ Var(A, B, ÿ ) The sample variance of all the elements in arrays A , B , ÿ
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CHEM 140L Session 7 - Data Analysis in Mathcad 7-3 Error Bars Mathcad’s X-Y plot function has the ability to add error bars to data plotted. The error bars are formed from 2 adjacent traces. One trace gives the lower limit of the error bar and the other trace gives the upper limit of the error bar. Consider a set of x-y data, with measurements taken on two samples. Using the statistical functions, the mean and standard deviation of each measure can be computed. Let us consider creating a plot average of the y data as a function of the x -data, displaying the error bars indicating the standard deviation for each measurement. We are required to define vectors which contain the upper and lower limits of the error bars. For this example, the vector yHi is defined as y avg + error and the vector yLo is defined as y avg - error . On the y -axis y avg , yHi and yLo are plotted.
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CHEM 140L Session 7 - Data Analysis in Mathcad 7-4 To display the error bars on the graph, access the Formatting Currently Selected X-Y Plot dialog box by double clicking anywhere on the graph. To access the trace formatting options, click the Trace tab. For this example, trace 1 , trace 2 and trace 3 represent y avg , yHi and yLo , respectively. Under the Type column, select error for trace 2 and trace 3 . The error bars should now be displayed on the graph.
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CHEM 140L Session 7 - Data Analysis in Mathcad 7-5 Interpolation Interpolation is the process by which the value of a variable is estimated from known values of that variable at other (normally nearby) points. Consider the example of experimental data consisting of temperatures taken at various times. If you wish to predict the temperature at a new time, there are two methods that you could use to make this prediction, namely regression and interpolation.
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CHEM%20140L%20Session%2007 - Session 07 Data Analysis in...

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