The next job is to convert the each list into a final best value uncertainty. At this point, the instructor can show the students a shortcut method for doing this. First, the best values are, as usual, the averages of our 12 numbers for each of the two cases (slow and fast). Next, instead of taking the time to draw a histogram, we simply note that 12/6 = 2 and so we eliminate the 2 largest measurements and the 2 smallest measurements. So simply cross out the outer 4 measurements, i.e, the two highest and the two lowest numbers. Of the 8 numbers left, circle the highest and the lowest. These circled numbers become the edges of our brackets, from which we write down the uncertainty. Below is an example, where all numbers are in ft/sec,

2.8 3.1 2.9 3.0 2.9 2.5 2.8 3.3 2.7 3.5 (3.2} 2.9 This gives us an uncertainty of 0.2 ft/sec. (That comes from 1/2(3.2 - 2.8)). The average of the 12 numbers is 2.97 ft/sec. So our result is 2.97 + 0.2 ft/sec. But, again from Rule 2, we must present our result as 3.0 + 0.2 ft/sec. Perhaps the two results will look something like this: (measured speed) = 3.0 + 0.2 ft/sec (slow walkers) (measured speed) = 4.7 + 0.3 ft/sec (fast walkers) The student should follow this procedure with the class data to get the final results for the measured speeds and record them on the data sheet. DISCUSSION: A discussion should include how we can conclude whether a real measurable difference exists between the two results, and how the measure of the uncertainty is important in reaching that conclusion. The instructor (and each student) should draw the two data points on the board (or on graph paper) to illustrate the idea: slow walkers last walkers 2.0 3.0 40 6.0 Ft/sec Questions 1. Rewrite the result below in its clearest form, with suitable numbers of significant figures: measured speed = 4.378 x 10' + 53 cm/sec. 2. Two students measure the length of the same pencil and report the results 146 + 3 mm and 148 +3 mm. Draw an illustration like that shown above (for slow and fast walkers) to represent these two measurements. Is the discrepancy between the two measurements significant? Why or why not? 3. (a) A student measures the diameter of a steel ball 5 times and gets the results (all in cm) 2.0, 2.2, 2.2, 2.1, and 2.0. What is your best estimate and uncertainty for the diameter? b) The student is told that the accepted value is 2.05 cm. Do you think the discrepancy between the student's best estimate and the accepted value is significant? Why or why not