138 CHAPTER 3 Describing, Exploring, and Comparing Data 3. z Score Using the differences from Exercise 1, find the z score corresponding to the difference of -11.2in. Is that difference significantly low, significantly high, or neither? 4. Boxplot Using the same differences from Exercise 1, construct a boxplot and include the values of the 5-number summary. 5.ER Codes In an analysis of activities that resulted in brain injuries presenting at hospital emergency rooms, the following activities were identified by the codes shown in parentheses: bicycling (12); football (14); playground (22); basketball (27); swimming (40). Find the mean of 12, 14, 22, 27, and 40. What is wrong with this result? 6. MCAT In a recent year, applicants to medical schools achieved scores on the Medical College Admission Test (MCAT) with a mean of 504.7 and a standard deviation of 9.4. Identify the MCAT scores that are significantly low or high. 7.Interpreting a Boxplot Shown below is a boxplot of a sample of 30 maximal skull widths (mm) measured from Egyptian skulls from around 4000 B.C. What do the numbers in the boxplot represent? 8. Estimating Standard Deviation Listed below are sorted weights (g) of a sample of M&M plain candies randomly selected from one bag. Use the range rule of thumb to estimate the value of the standard deviation of all 345 M&Ms in the bag. Compare the result to the standard deviation of 0.0366 g computed from all of the 345 M&Ms in the bag. 0.799 0.843 0.849 0.855 0.870 0.872 0.874 0.875 0.879 0.886 0.887 0.889 0.894 0.901 0.902 0.902 0.926 0.940 0.943 0.944 9. Percentiles Use the sorted weights of M&Ms from the preceding exercise to find the value of P25. How does the result compare to the value of Q1? 10. Comparing Birth Weights The birth weights of a sample of females have a mean of 3037.1 g and a standard deviation of 706.3 g. The birth weights of a sample of males have a mean of 3272.8 g and a standard deviation of 660.2 g (based on Data Set 6 “Births” in Appendix B). When considered among members of the same gender, which baby has the relatively larger birth weight: a female with a birth weight of 3200 g or a male with a birth weight of 3400 g? Why? 1. Sugar Listed below are measured weights (mg) of sugar in Domino packets labelled as containing 3500 mg (or 3.5 g). a. Are the data qualitative or quantitative? b. What is the level of measurement of the data (nominal, ordinal, interval, or ratio)? c. Before any rounding, are the weights discrete or continuous? d. Given that the weights are from Domino sugar packets selected from a much larger population, are the weights a sample or a population? e. If we calculate the mean of the listed values, is the result a statistic or a parameter? 3511 3516 3521 3531 3532 3545 3583 3588 3590 3617 3621 3635 3638 3643 3645 3647 3666 3673 3678 3723 Cumulative Review Exercises
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