Expressing Uncertainties of Experimental Data

•    In Column E of the worksheet is an example set of ten values of four-digit numbers that span a range of no more than ten (5555, 5556, 5557, 5558, 5559, 5560, 5561, 5562, 5563, and 5564).  For the example set the “ave ± sd” = 5560 ± 3.  Note that there are now additional rows showing the "sd/ave" (the relative uncertainty) in both fractional and percent form.  The percent uncertainty is less than a tenth of one percent. If these were your data from an experiment, you would be either an excellent experimentalist or very lucky!

•    Put into Column F a set of ten numbers with more variation, perhaps a range of one hundred, such that your standard deviation is a larger percentage of your average.  Change the input values until your percent uncertainty lies between one-tenth and one percent.  Express the "experimental data" using the standard form "ave ± sd" that was explained in Part I, and place your answer in the blue box.

•    Likewise, into Columns G and H, put in sets of ten numbers such that your percent uncertainities lie between one and ten percent, and ten and one hundred percent, respectively, expressing the experimental results in standard form.

•    Let’s summarize!  The whole point of this exercise is that in your lab work throughout this term you will often have to write down the results of some quantity that is based on many individual measurements that the computer characterizes by “ave” and “sd” values.  Then you will need to round off these values according to the rules given in Part I in order to communicate properly the results of your experiment.

•    In the mechanics laboratory, a ratio of better than 1% is probably blind luck, but if you are careful, you should usually be able to do better than 5%.  Anytime that ratio equals or exceeds 10%, you should repeat the measurement in more careful fashion because the equipment you are working is much more accurate than 10%.

•    Make sure to change the order of your name and your partner's name at the top of the worksheet for your respective copies.  Email them to yourselves such that you have a record of your work in case of any problems with submission for grading.  To submit them, each student must log on to the section's myWPI site, select Lab Submissions in the left-hand menu, click on the appropriate link, and attach the local file (your worksheet).  Internet Explorer is the most reliable means of submission.