IPS pg. 332 gives rules for variances. The rule for linear transformations is easy to demonstrate; however I am having problems with the addition of variances when adding data sets. It is fairly easy to show that the spreads of the values are additive and I am working on a spreadsheet simulation which should show that the variances are additive inductively. When I demonstrate this inductively I like to give an algebraic proof for those who can follow it but I cannot find/figure-out one. Can anyone help? How do you justify using the addition of variances when comparing two mean? I would be interested in any ideas you have for teaching this material to high school students.
John C. Chappelle email@example.com Brookstone School Tele: 706-660-9731 (W) 440 Bradley Park Dr Tele: 706-323-8307 (H) Columbus, Ga 31904-2989 FAX: 706-660-9731