91Ó°ÊÓ

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 $72.$

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

Mina is waiting in line at the Department of Motor Vehicles (DMV). Her wait time of $32$minutes is the ${85}^{th}$ percentile of wait times. Is that good or bad? Write a sentence interpreting the ${85}^{th}$ percentile in the context of this situation.

The following data represent the number of employees at various restaurants in New York City. Using this data, create a histogram.

$22;35;15;26;40;28;18;20;25;34;39;42;24;22;19;27;22;34;40;20;38;$and $28$

Use $10–19$as the first interval.