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For each of the following data sets, create a stem plot and identify any outliers. The miles per gallon rating for 30 cars are shown below (lowest to highest). 19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43

The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. Table 2.40 shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students. $$ \begin{array}{|l|l|}\hline \text { Seasons } & {\text { Number of students }} & {\text { Proportion of population }} \\ \hline \text { Spring } & {8} & {24 \%} \\ \hline \text { Summer } & {9} & {26 \%} \\ \hline \text { Autumn } & {11} & {32 \%} \\ \hline \text { Winter } & {6} & {18 \%} \\\ \hline\end{array} $$

The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to 1973. $$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Year } & {1961} & {1962} & {1963} & {1964} & {1965} & {1966} & {1967} \\ \hline \text { Police } & {260.35} & {269.8} & {272.04} & {272.96} & {272.51} & {261.34} & {268.89} \\\ \hline \text { Homicides } & {8.6} & {8.9} & {8.52} & {8.89} & {13.07} & {14.57} & {21.36} \\ \hline\end{array}$$ Table 2.52 $$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Year } & {1968} & {1969} & {1970} & {1971} & {1972} & {1973} \\ \hline \text { Police } & {295.99} & {319.87} & {341.43} & {356.59} & {376.69} & {390.19} \\ \hline \text { Homicides } & {28.03} & {31.49} & {37.39} & {46.26} & {47.24} & {52.33} \\\ \hline\end{array}$$ Table 2.53 a. Construct a double time series graph using a common \(x\) -axis for both sets of data. b. Which variable increased the fastest? Explain. c. Did Detroit's increase in police officers have an impact on the murder rate? Explain.

Listed are 29 ages for Academy Award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. Find the \(40^{\text { th }}\) percentile. b. Find the \(78^{\text { th }}\) percentile.

a. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race? b. The 20th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20th percentile in the context of the situation. c. A bicyclist in the 90th percentile of a bicycle race completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90th percentile in the context of the situation.

The University of California has two criteria used to set admission standards for freshman to be admitted to a college in the UC system: a. Students' GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an "admissions index" score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state. In this context, what percentile does the top 12% represent? b. Students whose GPAs are at or above the 96th percentile of all students at their high school are eligible (called eligible in the local context), even if they are not in the top 12% of all students in the state. What percentage of students from each high school are "eligible in the local context"?

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40 Identify the median.

Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right. 87; 87; 87; 87; 87; 88; 89; 89; 90; 91

The mean and median for the data are the same. 3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7 Is the data perfectly symmetrical? Why or why not?