1) the plot of monthly mean temperature over time for any one site is not going to be a Normal distribution - it is not a frequency plot/histogram type of plot. That the "mean temperature" from Jan to Jan in Bismarck, ND has the appearance of a Normal distribution is strictly an artifact of plotting - as someone pointed out by suggesting a plot from April to April. Sorry 'bout that.
2) the monthly "mean temperature" is actually the average of the daily "average." The daily average is the average of the daily high and daily low. Nobody I know measures the temperature every second, then computes the average for the day. Why should we expect the daily average to be Normally distributed? 3) thanks to the Central Limit Theorem, we can confidently predict that the monthly mean temperature, in one location, will be distributed Normally, for any given month, over many years. This approach was suggested by one person (sorry, I'm not up on references this am) who urged examination of one location with a frequency plot over a consistent time. 4) I once examined annual precipitation in Milwaukee's official station over a 100 year period. I cannot expect the distribution to be Normal, as the CLT is not invoked. However, I found that individual extremes were not evident, even when the station was moved closer to the local Lake. Even the frightfully dry summer of '88 did not pop out, since it rained a good deal in Oct.. For purposes of illustration to your students, I think the resultant distribution would be quite close enough to a Normal to satisfy them. I think I can find the data & ship it to those who are interested. 5) It might be highly informative for your students to have them figure out why some of these datasets are expected to be Normal, and some are not expected to be so. Cheers, Jay Stan Brown wrote: > My class is starting normal distributions today, and I asked them to > name some distributions and say whether they were normal. > > One student suggested seasons, such as high temperatures. Those are > more nearly cyclical, but then I got to wondering if there are any > seasonal or climate phenomena that are normally distributed. I can't > think of any, but I wonder if I'm overlooking an obvious example. > > Any suggestions? > > -- > Stan Brown, Oak Road Systems, Cortland County, New York, USA > http://OakRoadSystems.com > "Honesty always gives you the advantage of surprise." > -- /Yes, Prime Minister/ -- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
