SUPPLEMENTARY EXERCISES for ... - WH Freeman

Section 3 7S1.25 In 1995, the SATs were “recentered” to locate the mean scores for individuals close tothe center of the 200 to 800 range of possible scores. To see the effect of recentering, we enterthe state results for the mathematics and verbal SATs for both 1990 and 1996 into a statisticalsoftware package. Here are the results. (This output is from the Minitab statistical software;other software produces similar results.)SATV-1990N MEAN MEDIAN STDEV MIN MAX Q1 Q351 448.16 443.00 30.82 397.00 511.00 422.00 476.00SATM-1990N MEAN MEDIAN STDEV MIN MAX Q1 Q351 497.39 490.00 34.57 437.00 577.00 470.00 523.00SATV-1996N MEAN MEDIAN STDEV MIN MAX Q1 Q351 531.90 525.00 33.76 480.00 596.00 501.00 565.00SATM-1996N MEAN MEDIAN STDEV MIN MAX Q1 Q351 529.30 521.00 34.83 473.00 600.00 500.00 557.00Use the output to make side-by-side boxplots of the four distributions. What was the effect ofrecentering on the distribution of verbal SAT scores in the states? How did the distributions ofstate verbal and mathematics scores compare before recentering? How do they compare afterrecenteringS1.26 Give an approximate five-number summary of the salary data in Exercise S1.12 by pretendingthat all salaries fall at the midpoint of their class. You see that you can find approximatenumerical descriptions from grouped data when the actual data are not available.Section 3S1.27 The Environmental Protection Agency requires that the exhaust of each model of motorvehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) inthe exhaust of one light truck model was found to vary among individual trucks according to anormal distribution with mean µ = 1.45 grams per mile driven and standard deviation σ = 0.40grams per mile. Sketch the density curve of this normal distribution, with the scale of gramsper mile marked on the horizontal axis.S1.28 A study of elite distance runners found a mean weight of 63.1 kilograms (kg), with astandard deviation of 4.8 kg. Assuming that the distribution of weights is normal, sketch thedensity curve of the weight distribution with the horizontal axis marked in kilograms. (Basedon M. L. Pollock et al., “Body composition of elite class distance runners,” in P. Milvy (ed.),The Marathon: Physiological, Medical, Epidemiological, and Psychological Studies, New YorkAcademy of Sciences, 1977.)