91Ó°ÊÓ

The mean 2015 income for five families was \(\$ 99,520\). What was the total 2015 income of these five families?

When is the value of the standard deviation for a data set zero? Give one example. Calculate the standard deviation for the example and show that its value is zero.

The following data give the prices of seven textbooks randomly selected from a university bookstore. \(\begin{array}{lllllll}\$ 89 & \$ 170 & \$ 104 & \$ 113 & \$ 56 & \$ 161 & \$ 147\end{array}\) a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero? b. Calculate the range, variance, standard deviation and coefficient of variation.

The following data represent the systolic blood pressure reading (that is, the top number in the standard blood pressure reading) in \(\mathrm{mmHg}\) for each of 20 randomly selected middle-aged males who were taking blood pressure medication. \(\begin{array}{llllllllll}139 & 151 & 138 & 153 & 134 & 136 & 141 & 126 & 109 & 144 \\ 111 & 150 & 107 & 132 & 144 & 116 & 159 & 121 & 127 & 113\end{array}\) a. Calculate the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation.

The following data give the times (in minutes) that all 10 students took to complete an assignment in a statistics class. \(\begin{array}{llllllllll}15 & 26 & 16 & 36 & 31 & 13 & 29 & 18 & 21 & 39\end{array}\) a. Calculate the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation. c. What does the high value of the standard deviation tell you?

Are the values of the mean and standard deviation that are cal- culated using grouped data exact or approximate values of the mean and standard deviation, respectively? Explain.

Briefly explain Chebyshev's theorem and its applications.

A sample of 3000 observations has a bell-shaped distribution with a mean of 82 and a standard deviation of \(16 .\) Using the empirical rule, find the approximate percentage of the observations that fall in the intervals \(\bar{x} \pm 1 s, \bar{x} \pm 2 s\), and \(\bar{x} \pm 3 s\).

The one-way commuting times from home to work for all employees working at a large company have a mean of 34 minutes and a standard deviation of 8 minutes. a. Using Chebyshev's theorem, find the minimum percentage of employees at this company who have one-way commuting times in the following intervals. i. 14 to 54 minutes ii. 18 to 50 minutes 'b. Using Chebyshev's theorem, find the interval that contains one-way commuting times of at least \(89 \%\) of the employees at this company.

The one-way commuting times from home to work for all employees working at a large company have a bell-shaped curve with a mean of 34 minutes and a standard deviation of 8 minutes. Using the empirical rule, find the approximate percentages of the employees at this company who have one-way commuting times in the following intervals. a. 10 to 58 minutes b. 26 to 42 minutes c. 18 to 50 minutes