91Ó°ÊÓ

The prices of all college textbooks follow a bell-shaped distribution with a mean of \(\$ 180\) and a standard deviation of \(\$ 30\). a. Using the empirical rule, find the (approximate) percentage of all college textbooks with their prices between i. \(\$ 150\) and \(\$ 210\) ii. \(\$ 120\) and \(\$ 240\) b. Using the empirical rule, find the interval that contains the prices of (approximate) \(99.7 \%\) of college textbooks.

Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.

Explain how the interquartile range is calculated. Give one example.

The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84. $$ \begin{array}{lllllll} 73 & 75 & 69 & 68 & 78 & 69 & 74 \\ 76 & 72 & 79 & 68 & 77 & 71 & \end{array} $$ a. Find the values of the three quartiles and the interquartile range. b. Calculate the (approximate) value of the 35 th percentile. c. Compute the percentile rank of 71 .

The following data give the number of new cars sold at a dealership during a 20-day period. $$ \begin{array}{rrrrrrrrrr} 8 & 5 & 12 & 3 & 9 & 10 & 6 & 12 & 8 & 8 \\ 4 & 16 & 10 & 11 & 7 & 7 & 3 & 5 & 9 & 11 \end{array} $$ a. Calculate the values of the three quartiles and the interquartile range. Where does the value of 4 lie in relation to these quartiles? b. Find the (approximate) value of the 25 th percentile. Give a brief interpretation of this percentile. c. Find the percentile rank of 10 . Give a brief interpretation of this percentile rank.

The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers. \(\begin{array}{llllllllll}50 & 71 & 57 & 39 & 45 & 64 & 38 & 53 & 35 & 62 \\\ 74 & 40 & 67 & 44 & 77 & 61 & 58 & 55 & 64 & 59\end{array}\) a. Calculate the values of the three quartiles and the interquartile range. Where does the value 57 fall in relation to these quartiles? b. Find the approximate value of the 30 th percentile. Give a brief interpretation of this percentile. c. Calculate the percentile rank of 61 . Give a brief interpretation of this percentile rank.

Prepare a box-and-whisker plot for the following data: \(\begin{array}{llllllll}36 & 43 & 28 & 52 & 41 & 59 & 47 & 61 \\ 24 & 55 & 63 & 73 & 32 & 25 & 35 & 49 \\ 31 & 22 & 61 & 42 & 58 & 65 & 98 & 34\end{array}\) Does this data set contain any outliers?

The following data give the time (in minutes) that each of 20 students selected from a university waited in line at their bookstore to pay for their textbooks in the beginning of the Fall 2015 semester. \(\begin{array}{rrrrrrrrrr}15 & 8 & 23 & 21 & 5 & 17 & 31 & 22 & 34 & 6 \\ 5 & 10 & 14 & 17 & 16 & 25 & 30 & 3 & 31 & 19\end{array}\) Prepare a box-and-whisker plot. Comment on the skewness of these data.

The following data give the odometer mileage (rounded to the nearest thousand miles) for all 20 cars that are for sale at a dealership. \(\begin{array}{llllllllll}62 & 86 & 58 & 84 & 72 & 40 & 27 & 38 & 50 & 43 \\\ 27 & 40 & 90 & 43 & 94 & 36 & 28 & 48 & 86 & 77\end{array}\) a. Calculate the mean and median. Do these data have a mode? Why or why not? b. Calculate the \(10 \%\) trimmed mean for these data. c. Compute the range, variance, standard deviation, and coefficient of variation for these data.

The following data give the number of driving citations received during the last three years by 12 drivers. \(\begin{array}{llllllllllll}4 & 8 & 0 & 3 & 11 & 7 & 4 & 14 & 8 & 13 & 7 & 9\end{array}\) a. Find the mean, median, and mode for these data. b. Calculate the range, variance, and standard deviation. c. Are the values of the summary measures in parts a and \(\mathrm{b}\) population parameters or sample statistics?