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The San Luis Obispo Telegram-Tribune (October 1 . the two counties among these six in the middle of the sal- 1994) reported the following monthly salaries for superary range. Which measure of center determines this salary, visors from six different counties: \(\$ 5354\) (Kern), \(\$ 5166\) and what is its value? Why is the other measure of center (Monterey), \$4443 (Santa Cruz), \$4129 (Santa Barbara), featured in this section not as favorable to these super\(\$ 2500\) (Placer), and \$2220 (Merced). San Luis Obispo visors (although it might appeal to taxpayers)? County supervisors are supposed to be paid the average of

The San Luis Obispo Telegram-Tribune (November 29,1995 ) reported the values of the mean and median salary for major league baseball players for \(1995 .\) The values reported were \(\$ 1,110,766\) and \(\$ 275,000\). a. Which of the two given values do you think is the mean and which is the median? Explain your reasoning. b. The reported mean was computed using the salaries of all major league players in \(1995 .\) For the 1995 salaries, is the reported mean the population mean \(\mu\) or the sample mean \(\bar{x}\) ? Explain.

The paper cited in Exercise \(4.61\) also reported values of single-leg power for a low workload. The sample mean for \(n=13\) observations was \(\bar{x}=119.8\) (actually 119.7692), and the 14 th observation, somewhat of an outlier, was \(159 .\) What is the value of \(\bar{x}\) for the entire sample?

The article "Can We Really Walk Straight?" \((\) American Journal of Physical Anthropology \([1992]: 19-\) 27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target \(60 \mathrm{~m}\) away at normal speed. Consider the following data on cadence (number of strides per second): \(\begin{array}{llllllll}0.95 & 0.85 & 0.92 & 0.95 & 0.93 & 0.86 & 1.00 & 0.92 \\\ 0.85 & 0.81 & 0.78 & 0.93 & 0.93 & 1.05 & 0.93 & 1.06 \\ 1.06 & 0.96 & 0.81 & 0.96 & & & & \end{array}\) Use the methods developed in this chapter to summarize the data; include an interpretation or discussion wherever appropriate. (Note: The author of the paper used a rather sophisticated statistical analysis to conclude that people cannot walk in a straight line and suggested several explanations for this.)

Suppose that the distribution of scores on an exam is closely described by a normal curve with mean 100 . The 16 th percentile of this distribution is 80 . a. What is the 84 th percentile? b. What is the approximate value of the standard deviation of exam scores? c. What \(z\) score is associated with an exam score of 90 ? d. What percentile corresponds to an exam score of \(140 ?\) e. Do you think there were many scores below 40 ? Explain.