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Unformatted text preview: ehavior of the data on the graph, determine the best possible function to describe this data. After you have decided on the appropriate equation, you need to determine the constants of this equation so that it best fits the data. Although this can be done by trial and error, it is much more efficient to think of how the behavior of the equation 229 APPENDIX: SOFTWARE you have chosen depends on each parameter. Calculus can be a great help here. This can be a time-consuming task, so be patient. Now you need to estimate the uncertainty in your fit by deciding the range of other lines that could also fit your data. This method of estimating your uncertainty is described in the appendix Accuracy, Precision and Uncertainty. Slightly changing the values for each constant in turn will allow you to do this quickly. After you have computed your uncertainties, return to your best-fit line and use it as your fit by selecting Accept Fit in the Command Panel. 230 APPENDIX: SOFTWARE Excel - MAKING GRAPHS You will find that numerous exercises in this manual will require graphs. Microsoft Excel is a spreadsheet program that can create fourteen types of graphs, each of which have from two to ten different formats. This results in a maze of possibilities. There are help screens in Excel; however, this overview is covers the type of graph you should include in your lab reports. This is meant to be a brief introduction to the use of Microsoft Excel for graphing scientific data. If you are acquainted with Excel already, you should still skim through this appendix to learn about the type of graph to include in reports. Step 1. Input your measurements and highlight the data using your cursor. 231 APPENDIX: SOFTWARE Step 2. Click on the “Chart Wizard” on the toolbar. Step 3. Choose XY Scatter, not Line, from the list and click the “Next” button. 232 APPENDIX: SOFTWARE Step 4. Select the “Series in: Columns” option and click the “Next” button. Step 5. Fill in the chart title and axis labels, and click the “Next” button. 233 APPENDIX: SOFTWARE Step 6. Click the “Finish” button. Step 7. Your graph will appear on the worksheet. 234 APPENDIX: SOFTWARE Step 8. Click on the data points to highlight them. Step 9. Select “Add a Trendline” from the “Chart” menu. 235 APPENDIX: SOFTWARE Step 10. Choose the best type of trend line for your data. Step 11. The trend line will appear – is it a good fit to your data? 236 APPENDIX: SOFTWARE Step 12. If the equation of the line is needed, choose “Display equation on chart.” Step 13. The equation of the trend line should appear on your graph. 237 APPENDIX: SOFTWARE 238 Appendix: Significant Figures to determine the uncertainties in your measurements. Calculators make it possible to get an answer with a huge number of figures. Unfortunately, many of them are meaningless. For instance, if you needed to split $1.00 among three people, you could never give them each exactly $0.333333 … The same is true for measurements. If you use a meter stick with millimeter markings to measure the length of a key, as in Figure 1, you could not measure more precisely than a quarter or half or a third of a mm. Reporting a number like 5.37142712 cm would not only be meaningless, it would be misleading. What are significant figures? The number of significant figures tells the reader the precision of a measurement. Table 1 gives some examples. Table 1 Length (centimeters) 12.74 11.5 1.50 1.5 12.25345 0.8 0.05 Figure 1 Number of Significant Figures 4 3 3 2 7 1 1 One of the things that this table illustrates is that not all zeros are significant. For example, the zero in 0.8 is not significant, while the zero in 1.50 is significant. Only the zeros that appear after the first non-zero digit are significant. In your measurement, you can precisely determine the distance down to the nearest millimeter and then improve your precision by estimating the next figure. It is always assumed that the last figure in the number recorded is uncertain. So, you would report the length of the key as 5.37 cm. Since you estimated the 7, it is the uncertain figure. If you don't like estimating, you might be tempted to just give the number that you know best, namely 5.3 cm, but it is clear that 5.37 cm is a better report of the measurement. An estimate is always necessary to report the most precise measurement. When you quote a measurement, the reader will always assume that the last figure is an estimate. Quantifying that estimate is known as estimating uncertainties. Appendix C will illustrate how you might use those estimates A good rule is to always express your values in scientific notation. If you say that your friend lives 143 m from you, you are saying that you are sure of that distance to within a few meters (3 significant figures). What if you really only know the distance to a few tens of meters (2 significant figures)? Then you need to express the distance in scientific notation 1.4 x 102 m. Is it always better to have more figures? Consider the measurement of the length of the key shown in Fi...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.

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