Expressing Uncertainties of Experimental Data

•    If you have not yet opened the worksheet at the link below, do so now.  The columns of this Excel file accept numbers that you enter under the title “Numerical Values.”  The count of the number of entries is given under “Number,” along with the “Average” of all entries and the “Standard Deviation”, which is a measure of the amount of scatter among all the entry values, and will not provide a numerical value until you have entered at least two numbers into any column.

•    In the example in Column A, the values are: 1, 3, 5, 7, 9, and 11.  The average (ave) of this set is 6, and the standard deviation (sd) is 3.741… .  Note that the interval defined by “ave ± sd” includes most but not all of the numbers in this particular set.

•    In Column B enter the following numbers: 1, 2, 3, 4, 5, 6. Take note of the average and the standard deviation at the bottom of this column.  The standard form for communicating experimental results in this course is as follows:  Round the “sd” value to ONE digit (unless the lead digit is a 1, in which case you round the “sd” value to TWO digits), and then round the “ave” value to the same decimal place as the right-most digit of the “sd.”  Then write the results as “ave ± sd.”  For the given example in Column A, the “ave ± sd” = 6 ± 4.  For Column B the “ave ± sd” = 3.5 ± 1.9. 

•    Now express “ave ± sd” for two more (different) sets, six numbers each, of your own choosing in Columns C and D.  Be sure to type the corresponding properly rounded “ave ± sd” into the empty blue cells.