The mean value of the physical quantity, as well as the standard deviation of the mean, can be evaluated after a relatively large number of independent similar measurements have been carried out. These measured quantities in many cases serve as a basis for the calculation of other physical quantities of interest. In such situations the uncertainties associated with the directly measured quantities affect the overall uncertainty in the final quantity of interest. To estimate the end uncertainty we use the rules of error propagation. For example, the area of a table is 4 = LW. If we measure the widtH and lengthL many times to establish errors for each quantity: A WA L what will the error in the volunde 4 be when we multiply the average values of the two quantities together? Or, in the other words, how the error of area propagates. The rules of error propagations can be found in the power-point presentation: \"Error Propagation\". It is placed in Appendix A. In this lab error analysis practiced by measuring area of a lab table using 20-cm wood stick. Objectives: . to practice the concepts of significant figures, mean value, standard deviation of the mean, and normal distribution by making multiple measurements of the length and width of a table . to estimate and measure the area of the laboratory table and report it with the correct number of significant figures and in the correct format . to practice the propagation of errors by determining the uncertainty in the measurement of the area of the table . to understand the difference between precision and accuracy Equipment: 20-cm wood stick, lab table, Logger Pro software. Procedure: A student was asked to use 20 cm unmarked wood stick to take 50 measurements of length and width of the laboratory table, shown on the above picture. The collected data is provided in table 1. Table 1. Length and Width of the laboratory table. Based on the acquired data, use Logger Pro to find the mean value of each dimension and the standard deviation. Using these found values, calculate the standard error for each dimension; the value of area and its standard error. The final results should be reported in centimeters with the correct number of significant figures. How to find the mean value of each dimension and the standard deviation of the mean, using the Logger Pro: Open the Logger Pro software. The default file consists of a two-column table and a graph area. Double-click on the first column name and change its label to \"length\" with units \"cm.\" In the same way, change the name and units of the second column to \"width\" and \"cm,\" respectively. Lock Colurrn (Prevent Cel Editing Dats Type |'\\_r'\\-"n Use the statistics feature of Logger Pro to find the mean values for each dimension as well as the standard deviation. A\\ * LT A Hint: To get the statistical values (mean, standard deviation etc.) for a set of data put the same data on x- and y- axes of the graph and next press STAT button in the tool bar. Unless noted otherwise when you present any data in a graph form avoid lines connecting the data points in Logger Pro you change graph features by double-click on the graph window, then uncheck box "connect points". You should make two statistical graphs length vs length and width vs width. To add a new graph use: INSERTGRAPH. Using statistical data from the graphs, calculate the mean value of area of the table and standard deviation of the mean for each of the measured dimensions using equation (2). Use those values to propagate the error in area following rule 2 (product and devision) in the document "Basic Concept of Error Analysis in Appendix A. In Data Analysis section of the Lab Template show all your calculations on how you found the area of the lab table, error in each dimension and how the error in area was propagated. In the result section report major results with the correct number of significant figures. First, remember to report only one significant figure in the uncertainty. Secondly, report the mean value of the quantity and its uncertainty to the same number of decimal places. The rules of handling significant figures can also be found in the document "Basic Concepts of Error Analysis' or the PowerPoint presentation "Results and Uncertainties" that are available in the Appendix A. Follow the description in the Discussion to provide all the information required for full credit. Complete Lab Template and submit final lab report. "