Section 1
Measures of Center
For the data sets in Exercises $1-4$ calculate the mean, the median, and the mode. Locate these measures on a dotplot.$n=5$ measurements: 0,5,1,1,3
For the data sets calculate the mean, the median, and the mode. Locate these measures on a dotplot.$n=8$ measurements: 3,2,5,6,4,4,3,5
For the data sets calculate the mean, the median, and the mode. Locate these measures on a dotplot.$n=10$ measurements: 3,5,4,5,10,5,6,9,2,8
For the data sets calculate the mean, the median, and the mode. Locate these measures on a dotplot.$n=7$ measurements: 3,6,4,0,3,5,2
Symmetric or Skewed? Based on the values of the mean and the median, decide whether the data set is skewed right, skewed left, or approximately symmetric in Exercises $5-8 .$$$\bar{x}=6.2 ; m=10$$
Symmetric or Skewed? Based on the values of the mean and the median, decide whether the data set is skewed right, skewed left, or approximately symmetric.$$\bar{x}=5.38 ; m=5.34$$
Symmetric or Skewed? Based on the values of the mean and the median, decide whether the data set is skewed right, skewed left, or approximately symmetric.$$\bar{x}=127.5 ; m=58.4$$
Symmetric or Skewed? Based on the values of the mean and the median, decide whether the data set is skewed right, skewed left, or approximately symmetric.$$\bar{x}=279 ; m=350$$
Use these $n=24$ measurements to answer the questions in Exercises $9-10 .$$\begin{array}{llllll}4.5 & 3.2 & 3.5 & 3.9 & 3.5 & 3.9 \\ 4.3 & 4.8 & 3.6 & 3.3 & 4.3 & 4.2 \\ 3.9 & 3.7 & 4.3 & 4.4 & 3.4 & 4.2 \\ 4.4 & 4.0 & 3.6 & 3.5 & 3.9 & 4.0\end{array}$Find the sample mean and median.
Use these $n=24$ measurements to answer the questions in Exercises $9-10 .$$\begin{array}{llllll}4.5 & 3.2 & 3.5 & 3.9 & 3.5 & 3.9 \\ 4.3 & 4.8 & 3.6 & 3.3 & 4.3 & 4.2 \\ 3.9 & 3.7 & 4.3 & 4.4 & 3.4 & 4.2 \\ 4.4 & 4.0 & 3.6 & 3.5 & 3.9 & 4.0\end{array}$Is the data set symmetric or skewed? Explain.
Use these $n=15$ measurements to answer the questions in Exercises 11 and 12.53,61,58,56,58,60,54,54,62,58,60,58,56,56,58Calculate $\bar{x}, m,$ and the mode.
Use these $n=15$ measurements to answer the questions in Exercises 11 and 12.53,61,58,56,58,60,54,54,62,58,60,58,56,56,58Are the data skewed right, skewed left, or symmetric? Draw a dotplot to confirm your answer.
For the data sets in Exercises $13-15,$ find the mean, the median, and the mode. Comment on the skewness or symmetry of the data.The following data give the estimated prices of a 170-gram can or a 200-gram pouch of water-packed tuna for 14 different brands, based on prices paid nationally in supermarkets.$\begin{array}{rrrrrrr}.99 & 1.92 & 1.23 & .85 & .65 & .53 & 1.41 \\ 1.12 & .63 & .67 & .69 & .60 & .60 & .66\end{array}$
For the data sets find the mean, the median, and the mode. Comment on the skewness or symmetry of the data.A survey by Consumer Reports looked at the reliability of cars as the cars get older. They surveyed owners of cars that were 3 years old, and recorded the average yearly repair and maintenance costs (in dollars) for 15 different models of compact cars $^{2}$ :$\begin{array}{rrrrrrrrr}125 & 45 & 115 & 25 & 110 & 115 & 120 & 45 \\ 40 & 125 & 55 & 90 & 105 & 110 & 80 & \end{array}$
For the data sets find the mean, the median, and the mode. Comment on the skewness or symmetry of the data.In a psychology experiment, 10 subjects were given 5 minutes to complete a task. Their time on task (in seconds) is recorded.$\begin{array}{lllll}175 & 190 & 250 & 230 & 240 \\ 200 & 185 & 190 & 225 & 265\end{array}$
The cost of auto insurance in California is dependent on many variables, such as the city you live in, the number of cars you insure, and your insurance company. The website www.insurance. ca.gov reports the annual 2017 standard premium for a male, licensed for $6-8$ years, who drives a Honda Accord 20,000 to 24,000 kilometers per year and has no violations or accidents. $^{3}$$$\begin{array}{lcc}\hline \text { City } & \text { Allstate } & \text { 21st Century } \\\hline \text { Long Beach } & \$ 3447 & \$ 3156 \\\text { Pomona } & 3572 & 3108 \\\text { San Bernardino } & 3393 & 3110 \\\text { Moreno Valley } & 3492 & 3300 \\\hline\end{array}$$a. What is the average premium for Allstate Insurance?b. What is the average premium for 21st Century Insurance?c. If you were buying insurance, would you care about the average premium cost? If not, what would you want to know?
Most American households have one digital video recorder (DVR), and many have more than one. A sample of 25 households produced the following measurements on $x$, the number of DVRs in the household:$\begin{array}{lllll}1 & 0 & 2 & 1 & 1 \\ 1 & 0 & 2 & 1 & 0 \\ 0 & 1 & 2 & 3 & 2 \\ 1 & 1 & 1 & 0 & 1 \\ 3 & 1 & 0 & 1 & 1\end{array}$a. Is the distribution of $x$, the number of DVRs in a household, symmetric or skewed? Explain.b. Guess the value of the mode, the value of $x$ that occurs most frequently.c. Calculate the mean, the median, and the mode for these measurements.d. Draw a relative frequency histogram for the data. Locate the mean, the median, and the mode along the horizontal axis. Are your answers to parts a and b correct?
Ten of the 50 largest businesses in the United States, randomly selected from the Fortune $500,$ are listed as follows along with their revenues (in millions of dollars) $^{4}$ :$$\begin{array}{lr|lr}\hline \text { Company } & \text { Revenues } & \text { Company } & \text { Revenues } \\\hline \text {GeneralMotors } & \$ 166,380 & \text { Target } & \$ 69,495 \\\text { IBM } & 79,919 & \text { Morgan Stanley } & 37,949 \\\text { Bank of America } & 93,662 & \text { Johnson \& Johnson } & 71,890 \\\text { Home Depot } & 94,595 & \text { Apple } & 215,639 \\\text { Boeing } & 94,571 & \text { Exxon Mobil } & 205,004 \\\hline\end{array}$$a. Draw a stem and leaf plot for the data. Are the data skewed?b. Calculate the mean revenue for these 10 businesses. Calculate the median revenue.c. Which of the two measures in part b best describes the center of the data? Explain.
Does birth order have any effect on a person's personality? A report on a study by an MIT researcher indicates that later-born children are more likely to challenge the establishment, more open to new ideas, and more accepting of change. ${ }^{5}$ In fact, the number of later-born children is increasing. During the Depression years of the 1930 s, families averaged 2.5 children ( $59 \%$ later-born), whereas the parents of baby boomers averaged 3 to 4 children (68\% later-born). What does the author mean by an average of 2.5 children?
As professional sports teams become more and more profitable, the salaries paid to the players have also increased. In fact, many sports superstars are paid huge salaries. If you were asked to describe the distribution of players' salaries for several different professional sports, what measure of center would you choose? Why?
The tuition and fees (in thousands of dollars) for a sample of 21 four-year state-run colleges and universities are shown in the following table.$\begin{array}{rrrrrr}10.4 & 10.7 & 10.0 & 9.2 & 8.6 & 8.9 \\ 6.8 & 10.0 & 9.7 & 9.0 & 8.2 & \\ 13.0 & 6.8 & 6.5 & 6.4 & 12.0 & \\ 10.4 & 14.3 & 8.2 & 15.6 & 8.8 & \end{array}$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?
Searching online for the price of an item you would like to buy can save you quite a bit of money. A search for the best price for a white KitchenAid 5-speed hand mixer using yroo.com lists 16 sellers with various prices found in the following table.$$\begin{array}{lclc}\hline \text { Seller } & \text { Price (\$) } & \text { Seller } & \text { Price (\$) } \\\hline \text { Best Buy } & 39.99 & \text { Sears } & 39.99 \\\text { Blain's Farm \& Fleet } & 39.99 & \text { Boston Store } & 39.99 \\\text { Bergners } & 39.99 & \text { Home Depot } & 41.46 \\\text { Wayfair } & 42.46 & \text { Buydig.com } & 43.99 \\\text { Target } & 46.49 & \text { Shopko } & 47.49 \\\text { Jet.com } & 47.90 & \text { Amazon } & 47.19 \\\text { Walmart } & 51.97 & \text { Office Depot } & 54.99 \\\text { Houzz } & 59.99 & \text { True Value } & 59.99 \\\hline\end{array}$$a. What is the average price of this hand mixer for these 16 sellers?b. What is the median price for these 16 sellers?c. As a consumer would you be interested in the average price of the hand mixer? The median price? What other descriptive measures would be important to you?