Name: Chapters 1-6 Homework Worksheets

Chapter 2

1. Consider the following part of a data set:

List the variables in the data set. Indicate whether each variable is treated as categorical or quantitative in this data set. If the variable is quantitative, state the units.

For problems 2 & 3: Describe the W's (Who, What, When, Where, How, Why), if the information is given. If the information is not given, state that it is not specified. Also, list the variables. Indicate whether each variable is categorical or quantitative. If the variable is quantitative, tell the units.

2. The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and math, and any disabilities or special education needs.

3. One of the reasons that the Monitoring the Future (MTF) project was started was "to study changes in the beliefs, attitudes, and behavior of young people in the United States." Data are collected from 8th, 10th, and 12th graders each year. To get a representative nationwide sample, surveys are given to a randomly selected group of students. In Spring 2004, students were asked about alcohol, illegal drug, and cigarette use. Describe the W's, if the information is given. If the information is not given, state that it is not specified.

AP Statistics – Classwork Chapter 3

Smoking and Education

200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes. Results are summarized in the table.

Smoker / Non-Smoker / Total
High School / 32 / 61 / 93
2 yr college / 5 / 17 / 22
4+ yr college / 13 / 72 / 85
Total / 50 / 150 / 200

1. Discuss the W’s.

2. Identify the variables.

3. a) What percent of the shoppers were smokers with only high school educations? ______

b) What percent of the shoppers with only high school educations were smokers? ______

c) What percent of the smokers had only high school educations? ______

4. Create a segmented bar graph comparing education level

among smokers and non-smokers. Label your graph clearly

5. Do these data suggest there is an association between smoking and education level? Give statistical evidence to support your conclusion.

6. Follow-up question: Does this indicate that students who start smoking while in high school tend to give up the habit if they complete college? Explain.

7. Consider the following pie charts of a subset of the data below:

Do the pie charts above indicate that milk consumption by

young girls is independent of the nationwide survey year? Explain.

Has the percentage of young girls drinking milk changed over time? The following table is consistent with the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (Shanthy A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239):

Nationwide Food Survey Years
1987-1988 / 1989-1991 / 1994-1996 / Total
Drinks Fluid Milk / Yes / 354 / 502 / 366 / 1222
No / 226 / 335 / 366 / 927
Total / 580 / 837 / 732 / 2149

8. Identify the variables and tell whether each is categorical or quantitative.

9. Which of the W’s are unknown for these data?

10. Find the following:

a. What percent of the young girls reported that they drink milk?

b. What percent of the young girls were in the 1989-1991 survey?

c. What percent of the young girls who reported that they drink milk were in the 1989-1991 survey?

d. What percent of the young girls in 1989-1991 reported that they drink milk?

11. What is the marginal distribution of milk consumption?

12. Write a sentence or two about the conditional relative frequency of the people who said that they did not drink fluid milk.

13. Do you think that milk consumption by young girls is independent of the nationwide survey year? Use statistics to justify your reasoning.

Chapter 3 Extra Practice- Multiple Choice

1. Which one of the following variables is categorical?

a. the type of text book

b. the daily high temperature

c. the fraction of material in a statistics class understood by a student

d. the number of classes taken by a college freshman

e. the weight of babies born at a large hospital

2. Which of the following is the appropriate calculation to find the number of degrees in each portion of a pie graph?

a. d.

b. e. none are correct

Chapter 3 Free Response Practice

3. (2011A #2) The table below shows the political party registration by gender of all 500 registered voters in Franklin Township.

Party Registration- Franklin Township
Party W / Party X / Party Y / Total
Female / 60 / 120 / 120 / 300
Male / 28 / 124 / 48 / 200
Total / 88 / 244 / 168 / 500

(a) Given that a randomly selected registered voter is a male, what is the probability that he is registered for Party Y?

(b) Among the registered voters of Franklin Township, are the events “is a male” and “is registered for Party Y” independent? Justify your answer based on probabilities calculated from the table above.

graph, constructed from the data in the party registration–Franklin Township table, shows party-registration distributions for males and females in Franklin Township.

In Lawrence Township, the proportions of all registered voters for Parties W, X, and Y are the same as for Franklin Township, and party registration is independent of gender. Complete the graph below to show the distributions of party registration by gender in Lawrence Township.

3. 2010 #5

An advertising agency in a large city is conducting a survey of adults to investigate whether there is an association between highest level of educational achievement and primary source for news. The company takes a random sample of 2,500 adults in the city. The results are shown in the table below.

Highest Level of Educational Achievement
Primary Source for News / Not a H.S. Grad / H.S. Grad, but not a College Grad / College Grad / Total
Newspapers / 49 / 205 / 188 / 442
Local Television / 90 / 170 / 75 / 335
Cable Television / 113 / 496 / 147 / 756
Internet / 41 / 401 / 245 / 687
None / 77 / 165 / 38 / 280
Total / 370 / 1,437 / 693 / 2,500

(a) If an adult is to be selected at random from this sample, what is the probability that the selected adult is a college graduate or obtains news primarily from the internet?

(b) If an adult who is a college graduate is to be selected at random from this sample, what is the probability that the selected adult obtains news primarily from the internet?

(c) When selecting an adult at random from the sample of 2,500 adults, are the events “is a college graduate” and “obtains news primarily from the internet” independent? Justify your answer.

Chapter 4 Worksheet

1. The frequency table below shows the heights (in inches) of 130 members of a choir.

Height / 60 / 61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70 / 71 / 72 / 73 / 74 / 75 / 76
Count / 2 / 6 / 9 / 7 / 5 / 20 / 18 / 7 / 12 / 5 / 11 / 8 / 9 / 4 / 2 / 4 / 1

a. Find the median and IQR.

b. Find the mean and standard deviation

c. Display these data with a histogram.

d. Write a few sentences describing the distribution.

2. The following is a breakdown of win-loss records for SEC teams during the 2010 football season:

East West

South Carolina 9-5 Auburn 14-0

Florida 8-5 LSU 11-2

Georgia 6-7 Arkansas 10-3

Tennessee 6-7 Alabama 10-3

Kentucky 6-7 Mississippi State 9-4

Vanderbilt 2-10 Ole Miss 4-8

a. Make a 5-number summary for the win totals for SEC teams.

Minimum: Q1: Median: Q3: Maximum:

b. Find the Interquartile Range (IQR) for the win totals.

c. Find the mean and standard deviation for win totals.

d. Display the data with the following pictures:

i. Histogram ii. Stem and Leaf Plot iii. Dotplot

e. Describe the center of the data. (What’s the best measure? Mean/Median?)

f. Describe anything unusual in the data. (Any outliers/gaps?)

g. Describe the spread of the data. (Range, IQR or standard deviation?)

h. Describe the shape of the data. (Is it symmetric? skewed? Unimodal/bimodal/multimodal/uniform?)

3. The following table shows Electoral College votes by state. You also need to include Washington D.C. with your data, they have 3 electoral votes.

State / # / State / # / State / # / State / # / State / #
AL / 9 / HI / 4 / MA / 12 / NM / 5 / SD / 3
AK / 3 / ID / 4 / MI / 17 / NY / 31 / TN / 11
AZ / 10 / IL / 21 / MN / 10 / NC / 15 / TX / 34
AR / 6 / IN / 11 / MS / 6 / ND / 3 / UT / 5
CA / 55 / IA / 7 / MO / 11 / OH / 20 / VT / 3
CO / 9 / KS / 6 / MT / 3 / OK / 7 / VA / 13
CN / 7 / KY / 8 / NE / 5 / OR / 7 / WA / 11
DE / 3 / LA / 9 / NV / 5 / PA / 21 / WV / 5
FL / 27 / ME / 4 / NH / 4 / RI / 4 / WI / 10
GA / 15 / MD / 10 / NJ / 15 / SC / 8 / WY / 3

a. Make a 5-number summary for the electoral votes for each state (including DC).

Minimum: Q1: Median: Q3: Maximum:

b. Find the Interquartile Range (IQR) for the Electoral College votes.

c. Find the mean and standard deviation for the Electoral College votes.

d. Display the data with the following pictures:

i. Histogram ii. Stem and Leaf Plot

e. Describe the center of the data. (What’s the best measure? Mean/Median?)

f. Describe anything unusual in the data. (Any outliers/gaps?)

g. Describe the spread of the data. (Range, IQR or standard deviation?)

h. Describe the shape of the data. (Is it symmetric? skewed? Unimodal/bimodal/multimodal/uniform?)

4. Listed below are the final regular season standings for the 2010 NFL season.

NFC Teams / Win-Loss Record / AFC Teams / Win-Loss Record
Atlanta / 13-3 / New England / 14-2
Chicago / 11-5 / Pittsburgh / 12-4
New Orleans / 11-5 / Baltimore / 12-4
Philadelphia / 10-6 / NY Jets / 11-5
Green Bay / 10-6 / Indianapolis / 10-6
NY Giants / 10-6 / Kansas City / 10-6
Tampa Bay / 10-6 / San Diego / 9-7
Seattle / 7-9 / Jacksonville / 8-8
St. Louis / 7-9 / Oakland / 8-8
Minnesota / 6-10 / Miami / 7-9
Detroit / 6-10 / Houston / 6-10
Dallas / 6-10 / Tennessee / 6-10
Washington / 6-10 / Cleveland / 5-11
San Francisco / 6-10 / Cincinnati / 4-12
Arizona / 5-11 / Denver / 4-12
Carolina / 2-14 / Buffalo / 4-12

a. Sketch a histogram for the wins. b. Find the mean and standard deviation for the win totals

c. Is it appropriate to use the mean and d. Describe the associations of win totals.

standard deviations to summarize the data?

5. Mr. Hubbard collected data from his students about how many times that “tweet” a day on their

Twitter accounts. Out of all his students, the highest number of tweets per day was 16. Today, Mr.

Hubbard got a new student in his Algebra 1 class. Mr. Hubbard asked the student how many times they

tweeted in a day and the student said 25. If Mr. Hubbard were to include the new student’s total into his

data, would it cause the following summary statistics to increase, decrease, or stay about the same.

a. Mean: ______

b. Median: ______

c. Range: ______

d. IQR: ______

e. standard deviation: ______

Chapter 4 Multiple Choice

6. The figure above shows a cumulative relative frequency

histogram of 40 scores on a test given in an AP Statistics class.

Which of the following conclusions can be made from the graph?

(A) There is greater variability in the lower 20 test scores than in the higher 20 test scores.

(B) The median test score is less than 50.

(D) If the passing score is 70, most students did not pass the test.

(E) The horizontal nature of the graph for the test scores of 60 and below indicates that those scores occurred most frequently.

Chapter 4 Free Response Review

7. (2007B- #1) The Better Business Council of a large city has concluded that students in the city’s schools are not learning enough about economics to function in the modern world. These findings were based on test results from a random sample of 20 12th grade students who completed a 46-question multiple-choice test on basic economics concepts. The data set below shows the number of questions that each of the 20 students answered correctly:

12 16 18 17 18 33 41 44 38 35

19 36 19 13 43 8 16 14 10 9

a. Display these data in a stemplot

b. Use your stemplot from part (a) to describe the main features of this score distribution.

c. Why would it be misleading to report only a measure of center for this score distribution?

8. (2005B- #1) The graph below displays the scores of 32 students on a recent exam. Scores on this exam ranged from 64 to 95 points

6 * *

7 * * *

7 * * * *

8 * * * *

8 * * * * * *

9 * * * * * * *

9 * * * *

a. Describe the shape of this distribution

b. In order to motivate her students, the instructor of the class wants to report that, overall, the class’s performance on the exam was high. Which summary statistic, the mean or the median, should the instructor use to report that overall exam performance was high? Explain.

c. The midrange is defined as . Compute this value using the data above. Is the midrange considered a measure of center or a measure of spread? Explain.

Mooseburgers / McTofu
Al $123 / Ken $110
Boris $136 / Latisha $115
Connie $144 / Maria $130
Dwight $150 / Nate $100
Ernie $110 / Otto $120
Francois $131 / Pablo $146
Gloria $140 / Quentin $117
Horace $160 / Sally $360
Issac $120 / Ted $132
Juan $130 / Uta $107

Chapter 5