91Ó°ÊÓ

A data set has values ranging from a low of 10 to a high of \(50 .\) What's wrong with using the class limits \(10-20,20-30,30-40,40-50\) for a frequency table?

How do college professors spend their time? The National Education Association Almanac of Higher Education gives the following average distribution of professional time allocation: teaching, \(51 \% ;\) research, \(16 \% ;\) professional growth, \(5 \% ;\) community service, \(11 \% ;\) service to the college, \(11 \%\); and consulting outside the college, \(6 \% .\) Make a pie chart showing the allocation of professional time for college professors.

The following data represent annual salaries, in thousands of dollars, for employees of a small company. Notice that the data have been sorted in increasing order. $$\begin{array}{ccccccccccccc} 54 & 55 & 55 & 57 & 57 & 59 & 60 & 65 & 65 & 65 & 66 & 68 & 68 \\ 69 & 69 & 70 & 70 & 70 & 75 & 75 & 75 & 75 & 77 & 82 & 82 & 82 \\ 88 & 89 & 89 & 91 & 91 & 97 & 98 & 98 & 98 & 280 & & \end{array}$$ (a) Make a histogram using the class boundaries 53.5,99.5,145.5,191.5 237.5,283.5 (b) Look at the last data value. Does it appear to be an outlier? Could this be the owner's salary? (c) Eliminate the high salary of 280 thousand dollars. Make a new histogram using the class boundaries \(53.5,62.5,71.5,80.5,89.5,98.5 .\) Does this histogram reflect the salary distribution of most of the employees better than the histogram in part (a)?

How does average height for boys change as boys get older? According to Physician's Handbook, the average heights at different ages are as follows: $$\begin{array}{|l|llllllll|} \hline \text { Age (years) } & 0.5 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Height (inches) } & 26 & 29 & 33 & 36 & 39 & 42 & 45 & 47 \\ \hline \end{array}$$ $$\begin{array}{l|ccccccc} \hline \text { Age (years) } & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\ \hline \text { Height (inches) } & 50 & 52 & 54 & 56 & 58 & 60 & 62 \\ \hline \end{array}$$ Make a time-series graph for average height for ages 0.5 through 14 years.

Batting Averages The following data represent baseball batting averages for a random sample of National League players near the end of the baseball season. The data are from the baseball statistics section of the Denver Post $$\begin{aligned} &\begin{array}{cccccccc} 0.194 & 0.258 & 0.190 & 0.291 & 0.158 & 0.295 & 0.261 & 0.250 & 0.181 \end{array}\\\ &\begin{array}{cccccccc} 0.125 & 0.107 & 0.260 & 0.309 & 0.309 & 0.276 & 0.287 & 0.317 & 0.252 \end{array}\\\ &\begin{array}{ccccccc} 0.215 & 0.250 & 0.246 & 0.260 & 0.265 & 0.182 & 0.113 & 0.200 \end{array} \end{aligned}$$ (a) Multiply each data value by 1000 to "clear" the decimals. (b) Use the standard procedures of this section to make a frequency table and histogram with your whole-number data. Use five classes. (c) Divide class limits, class boundaries, and class midpoints by 1000 to get back to your original data.