Chapter 2: Descriptive Statistics

Listed are $32$ages for Academy Award winning best actors in order from smallest to largest. $18;18;21;22;25;26;27;29;30;31;31;33;36;37;37;41;42;47;52;55;57;58;62;64;67;69;71;72;73;74;76;77$a. Find the percentile of $37$.

b. Find the percentile of $72.$

In a survey, $40$people were asked how many times per year they had their car in the shop for repairs. The results are shown in Table $2.8.$Construct a line graph.

Jesse was ranked $37th$ in his graduating class of $180$ students. At what percentile is Jesse’s ranking?

The population in Park City is made up of children, working-age adults, and retirees. Table $2.10$shows the three age groups, the number of people in the town from each age group, and the proportion (%) of people in each age group. Construct a bar graph showing the proportions.

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.

Park city is broken down into six voting districts. The table shows the percent of the total registered voter

population that lives in each district as well as the percent total of the entire population that lives in each district. Construct a bar graph that shows the registered voter population by district.

a. For runners in a race, a higher speed means a faster run. Is it more desirable to have a speed with a high or a low percentile when running a race?

b. The $40th$ percentile of speeds in a particular race is$7.5$ miles per hour. Write a sentence interpreting the $40th$ percentile in the context of the situation.

The following data are the shoe sizes of $50$male students. The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars.

$$\begin{gathered} 9;9;9.5;9.5;10;10;10;10;10;10;10.5;10.5;10.5;10.5;10.5;10.5;10.5;10.5 \\ 11;11;11;11;11;11;11;11;11;11;11;11;11;11.5;11.5;11.5;11.5;11.5;11.5;11.5 \\ 12;12;12;12;12;12;12;12.5;12.5;12.5;12.5;14 \end{gathered}$$

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain

The following data are the number of sports played by $50$student athletes. The number of sports is discrete data since sports are counted.

$$\begin{gathered} 1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1 \\ 2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2 \\ 3;3;3;3;3;3;3;3 \end{gathered}$$

$20$student athletes play one sport. $22$student athletes play two sports. Eight student athletes play three sports.

Fill in the blanks for the following sentence. Since the data consist of the numbers $1,2,3,$and the starting point is $0.5$,

a width of one places the 1 in the middle of the interval $0.5$to _____, the $2$in the middle of the interval from _____ to

_____, and the $3$in the middle of the interval from _____ to _____.