Question

section 12.1 sampling, frequency distributions, and graphs 691

1. construct a stem - and - leaf plot for the data in exercise 19 showing the ages at which u.s. presidents were inaugurated.
2. a random sample of 40 college professors is selected from all professors at a university. the following list gives their ages:

63,48,42,42,38,59,41,44,45,28,54,62,51,44,63,66,59,46,51,28,37,66,42,40,30,31,48,32,29,42,63,37,36,47,25,34,49,30,35,50.
construct a stem - and - leaf plot for the data. what does the shape of the display reveal about the ages of the professors?

1. in “ages of oscar - winning best actors and actresses” (mathematics teacher magazine) by richard brown and gretchen davis, the stem - and - leaf plots shown compare the ages of actors and actresses for 30 winners of the oscar at the time they won the award.

actors stems actresses
2 14667
98753221 3 00113344455778
88776543322100 4 11129
6651 5
210 6 011
6 7 4
8 0
a. what is the age of the youngest actor to win an oscar?
b. what is the age difference between the oldest and the youngest actress to win an oscar?
c. what is the oldest age shared by two actors to win an oscar?
d. what differences do you observe between the two stem - and - leaf plots? what explanations can you offer for these differences?
in exercises 29 - 33, describe what is misleading in each visual display of data.

1. world population, in billions
2. book title output in the united states

190,078
172,000
171,061
147,120
114,487
source: r.r. bowker

1. percentage of the world’s computers in use, by country

u.s. 29%
china 4%
france 4%
japan 9%
uk 5%
germany 6%
source: computer industry almanac

1. enrollment at the university of georgia

total students african americans
33,878 33,405
32,941
32,317
31,288
2000 2001 2002 2003 2004
source: university of georgia office of institutional research

Explanation:

Step1: Identify youngest actor age

From the stem - and - leaf plot for actors, the youngest age is in the stem 3 row with the smallest leaf value. The youngest actor's age is 31.

Step2: Identify oldest and youngest actress ages

For actresses, the youngest age is in the stem 2 row, which is 21. The oldest age is in the stem 8 row, which is 80.

Step3: Calculate age difference for actresses

The age difference between the oldest and youngest actress is $80 - 21=59$.

Step4: Identify oldest shared age for actors

Looking at the actor's stem - and - leaf plot, the oldest age shared by two actors is 44 (in the stem 4 row, there are two 4s as leaves).

Step5: Analyze differences between plots

Differences: The ages of actors are more concentrated in the 30 - 50 range, while actresses have a wider spread from 20s to 80s. Explanation: This could be due to differences in the types of roles available for men and women in the film industry, or differences in how age is perceived and valued for male and female actors in the context of award - winning performances.

Answer:

a. 31
b. 59
c. 44
d. Differences: Ages of actors are more concentrated in 30 - 50 range, actresses have wider spread from 20s - 80s. Explanation: Could be due to role availability and age perception in film industry.