91Ó°ÊÓ

You are given \(n=5\) measurements: 0,5,1,1,3 . a. Draw a dotplot for the data. (HINT: If two measurements are the same, place one dot above the other.) Guess the approximate "center." b. Find the mean, median, and mode. c. Locate the three measures of center on the dotplot in part a. Based on the relative positions of the mean and median, are the measurements symmetric or skewed?

You are given \(n=10\) measurements: 3,5,4,6 , 10,5,6,9,2,8 a. Calculate \(\bar{x}\). b. Find \(m\). c. Find the mode.

The cost of automobile insurance has become a sore subject in California because insurance rates are dependent on so many different variables, such as the city in which you live, the number of cars you insure, and the company with which you are insured. The website www.insurance.ca.gov reports the annual 2006-2007 premium for a single male, licensed for \(6-8\) years, who drives a Honda Accord 12,600 to 15,000 miles per year and has no violations or accidents. $$ \begin{array}{lcc} \text { City } & \text { Allstate } & \text { 21st Century } \\ \hline \text { Long Beach } & \$ 2617 & \$ 2228 \\ \text { Pomona } & 2305 & 2098 \\ \text { San Bernardino } & 2286 & 2064 \\ \text { Moreno Valley } & 2247 & 1890 \end{array} $$ a. What is the average premium for Allstate Insurance? b. What is the average premium for 21 st Century Insurance? c. If you were a consumer, would you be interested in the average premium cost? If not, what would you be interested in?

n a psychological experiment, the time on task was recorded for 10 subjects under a 5-minute time constraint. These measurements are in seconds: $$ \begin{array}{lllll} 175 & 190 & 250 & 230 & 240 \\ 200 & 185 & 190 & 225 & 265 \end{array} $$ a. Find the average time on task. b. Find the median time on task. c. If you were writing a report to describe these data, which measure of central tendency would you use? Explain.

The number of Starbucks coffee shops in 18 cities within 20 miles of the University of California, Riverside is shown in the following table (www.starbucks.com). $$ \begin{array}{rrrrr} 16 & 7 & 2 & 6 & 4 \\ 1 & 7 & 1 & 1 & 1 \\ 3 & 2 & 11 & 1 & \\ 5 & 1 & 4 & 12 & \end{array} $$ a. Find the mean, the median, and the mode. b. Compare the median and the mean. What can you say about the shape of this distribution? c. Draw a dotplot for the data. Does this confirm your conclusion about the shape of the distribution from part b?

A set of data has a mean of 75 and a standard deviation of \(5 .\) You know nothing else about the size of the data set or the shape of the data distribution. a. What can you say about the proportion of measurements that fall between 60 and \(90 ?\) b. What can you say about the proportion of measurements that fall between 65 and \(85 ?\) c. What can you say about the proportion of measurements that are less than \(65 ?\)

Is your breathing rate normal? Actually, there is no standard breathing rate for humans. It can vary from as low as 4 breaths per minute to as high as 70 or 75 for a person engaged in strenuous exercise. Suppose that the resting breathing rates for college-age students have a relative frequency distribution that is mound-shaped, with a mean equal to 12 and a standard deviation of 2.3 breaths per minute. What fraction of all students would have breathing rates in the following intervals? a. 9.7 to 14.3 breaths per minute b. 7.4 to 16.6 breaths per minute c. More than 18.9 or less than 5.1 breaths per minute

To estimate the amount of lumber in a tract of timber, an owner decided to count the number of trees with diameters exceeding 12 inches in randomly selected 50 -by-50foot squares. Seventy 50 -by-50-foot squares were chosen, and the selected trees were counted in each tract. The data are listed here: $$ \begin{array}{rrrrrrrrrr} 7 & 8 & 7 & 10 & 4 & 8 & 6 & 8 & 9 & 10 \\ 9 & 6 & 4 & 9 & 10 & 9 & 8 & 8 & 7 & 9 \\ 3 & 9 & 5 & 9 & 9 & 8 & 7 & 5 & 8 & 8 \\ 10 & 2 & 7 & 4 & 8 & 5 & 10 & 7 & 7 & 7 \\ 9 & 6 & 8 & 8 & 8 & 7 & 8 & 9 & 6 & 8 \\ 6 & 11 & 9 & 11 & 7 & 7 & 11 & 7 & 9 & 13 \\ 10 & 8 & 8 & 5 & 9 & 9 & 8 & 5 & 9 & 8 \end{array} $$ a. Construct a relative frequency histogram to describe the data. b. Calculate the sample mean \(\bar{x}\) as an estimate of \(\mu,\) the mean number of timber trees for all 50 -by-50-foot squares in the tract. c. Calculate \(s\) for the data. Construct the intervals \(\bar{x} \pm\) \(s, \bar{x} \pm 2 s\), and \(\bar{x} \pm 3 s\). Calculate the percentage of squares falling into each of the three intervals, and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem.

The number of passes completed by Brett Favre, quarterback for the Green Bay Packers, was recorded for each of the 16 regular season games in the fall of 2006 (www.espn.com). \(^{9}\) $$ \begin{array}{rrrrrr} 15 & 31 & 25 & 22 & 22 & 19 \\ 17 & 28 & 24 & 5 & 22 & 24 \\ 22 & 20 & 26 & 21 & & \end{array} $$ a. Draw a stem and leaf plot to describe the data. b. Calculate the mean and standard deviation for Brett Favre's per game pass completions. c. What proportion of the measurements lie within two standard deviations of the mean?

Construct a box plot for these data and identify any outliers: $$ 25,22,26,23,27,26,28,18,25,24,12 $$