Temperatures

This exercise compares the high temperatures of six sites (Ogla, Wash; Belle Glade, Fla; Mexia, Tex; Mayville, N.D.; Minneapolis, Minn; and Hoopeston, Ill.) using numerical and graphical summaries. Click on Data under Chapter 2 in the left panel and then select Open remote ... under the File menu in the right panel. Select temps.xml from the Open File Dialog and click OK. Note that both Mayville and Minneapolis are assigned the Y role by default, whereas Date is assigned the Label role.

1. Select y|z from the Graph menu (conditioning z variables are not assigned here). Increase the number of bars in each histogram so that the class intervals span 5 degrees. Are the high-temperature histograms of Mayville and Minneapolis similar or different? Are the histograms bell-shaped or are they bimodal (two clusters of temperatures). If bimodal, what do these clusters represent? Are the mean values and spreads (standard deviations) similar? Explain.
2. Are the extreme values similar? What date was the coldest (in terms of the daily high) in Mayville? Is this the coldest date in Minneapolis also? How cold did it get in Mayville and Minneapolis?
3. Close the histogram for Mayville and change the Column Roles of Mayville and Minneapolis to None and of Olga to Y. Increase the number of bars in the Olga histogram so that the class intervals span 5 degrees. Are the shapes of the Olga and Minneapolis histograms different? If so, in what way? Which city has the more extreme high temperatures?
4. Looking at the histograms, do both cities have approximately the same mean high temperatures? What are the numerical values of the means? Do the mean values tell the whole story? Compare and comment on the standard deviations of the high temperatures?
5. Close the histogram for Minneapolis and change the Column Roles of Ogla to None and that of Belle Glade to Y. Increase the number of bars in the Belle Glade histogram so that the class intervals span about 2.5 degrees. Are the shapes of the Olga and Belle Glade histograms different? If so, in what way? Compare the means and spreads (standard deviations) of the two cities.
6. Do the same analysis for the preceding part except compare Mexia and Belle Glade.
7. Histograms that have one peak are called unimodal (because they have just one peak), and those with two peaks (or clusters) are called bimodal. Bimodal histograms are often mixtures of two different populations, such as men's and women's heights. For each of the six cities, decide whether it has a HIGH or MODERATE mean temperature, a LARGE or SMALL spread, and a UNIMODAL or BIMODAL spread.
8. Group the cities by the three characteristics in the preceding part. What do these cities have in common (other than similar high-temperature distributions).