1. Consider a hypothetical list of exam grades for a large lecture class. Find the mean, median, most probable value and standard deviation of this distribution of 100 grades. Quote your results to three significant figures. You may perform the calculation by hand, write your own program, or use a software package (such as Excel) to do the calculations for you, but you must show your work by explaining how you would calculate each quantity. Here is the data in text and excel formats.
2. Find the uncertainty in x as a function of the uncertainties in u and v for the following functions. This question should be answered in analytical form. Show your work. You may assume that u and v are completely uncorrelated. If you find it to be more convenient, you may express your result as a relative error in x (i.e. sigma_x/x).
a) x = 1/[2(u+v)]
b) x = 1/[2(u-v)]
c) x = 1/u^2
d) x = u v^2
e) x = u^2 + v^2
3. Derive a formula for making a linear fit to data with an intercept at the origin so that y = bx. Apply your method to fit a straight line through the origin to the following set of data (text or xls). Assume uniform uncertainties of si=2.0 in yi. Find the reduced chi-squared for the fit and the uncertainty in b. Note, do this problem analytically, i.e., do not use packaged fitting routines! You may use a spreadsheet, but you must show the formulas for each column!