AP STATISTICS Unit 2: Modeling Distributions of Data
Enduring understanding (Big Idea): Students will understand how to determine the location of an observation in a set of data; and understand the
normal distribution, including standardizing (transforming) the data.
Essential Questions:
1. Given an overall pattern from a large number of observations, how
can we describe it by a mathematical model?
2. What is a density curve and what information can it give us?
3. What is the normal distribution and how do we describe it? What
are its key properties?
4. How can we describe the location (i.e. position) of an observation in a set
of data?
5. What are a) Percentiles and b) z-scores? What is a common use for both?
6. What is standardizing data and why do we do it?
7. How do we transform data and why do we do it?
BY THE END OF THIS UNIT:
Students will know:
(See the AP Statistics Course Description page 7 for full details)
I. Exploring Data: Describing patterns and departures from patterns (20%–
30%)
A Constructing and interpreting graphical displays of distributions of univariate
data (… cumulative frequency plot) …
B Summarizing distributions of univariate data: Measuring position…percentile,
standardized scores (z-scores) & the effect of changing units on summary
measures
III Anticipating Patterns: Exploring random phenomena using probability and
simulation (20%–30%)
A See Unit 6 B. See Unit 7 C The normal distribution Properties of the normal
distribution, using tables of normal distribution, as a model for measurements
Unit Resources:
 Use of Fathom is highly recommended
http://www.keycurriculum.com/products/fathom
 Use Applets from: http://www.whfreeman.com/tps4e
http://www.rossmanchance.com/applets/
http://teachers.dadeschools.net/akoski/statsSyllabus1.htm
 Download the chapter glossary at (below) and give copies to your kids.
http://bcs.whfreeman.com/tps4e/#628644__666335__
Students will be able to…
1. to locate individual values within distributions of data.
2. interpret a cumulative relative frequency graph
3. find the standardized value (Z – score) of an observation. Interpret Z
scores in context
4. describe the effect of adding, subtracting, multiplying by, or dividing by a
constant on the shape, center, and spread of a distribution of data
5. approximately locate the median (equal-areas point) and the mean
(balance point) on a density curve
Vocabulary: Cumulative Relative Frequency Graph (See OJIVE below), Density
Curves, Empirical rule (68-95-99.7), Location in a distribution, Normal Curve,
Normal Distribution, Normal Probability (Quantile) plot, OJIVE (See CRFG above),
Percentile, Standard normal distribution, Standard normal table (Table A),
Standardize Variable (see z-score), Standardizing, Transforming Data, z-score (see
Standardize Variable)
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
Learning Tasks: homework - see page 2-6 of the Teacher's Edition
Performance Task: end the chapter with a "FRAPPY" (see Formative Assessments
and Problem Task suggestions below)
8. Look for and express regularity
Project: "Characterizing Students II"
Unit Review Game: Jeopardy and Millionaire (PowerPoints)
http://www.apstatsmonkey.com/StatsMonkey/TPS3e.html
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
in repeated reasoning
AP STATISTICS Unit 2: Modeling Distributions of Data
CORE CONTENT
Cluster Title: none
Standards: (CCSS: none)
NCSCOC 2.01 Construct and interpret graphical displays of univariate data
AP Stats IA Constructing and interpreting graphical displays of distributions of univariate data (… cumulative frequency plot) …
AP Stats IB3 Summarizing distributions of univariate data: Measuring position…percentiles, standardized scores(z-scores)
AP Stats IB5 The effect of changing units on summary measures
Concepts and Skills to Master (on paper and with technology)
Section 2.1 [Describing Location in a Distribution]
 Measuring position: Percentiles
 Transforming Data
 Density Curves
 Cumulative Relative Frequency Graphs (Ojives)
 Measuring position: z-scores
 Describing Density Curves
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Previous Skills and concepts in this course from Chapter 1
Academic Vocabulary
Cumulative Relative Frequency Graph (Also called an OJIVE), Density Curves, Location in a distribution, Percentile, Standardize Variable (see z-score),
Standardizing, Transforming Data, z-score (see Standardize Variable)
Suggested Instructional Strategies







Rely on the Teachers' Edition and the Platinum Resource Binder
The text is excellent and students should have their book (and their calculator) at each class.
The challenge is how to inspire kids to read and study it. There should be class discussions
during each class using material from the book and using the calculator. Consider assigning
the next class' material as a prereading. Especially focus on the boxes labeled "AP Exam
Common Error" in the margins (and also in Appendix A)
With all students on their calculators and you on your projection calculator do Technology
Corner 2.1 on page 16 using calculator lists (or other Technology)
Do Activity "Where do I Stand" on page 84
Have a Class Discussion of Section 2.1's "Summary" on page 104
The College Board has posted tremendously helpful material
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use:
http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for FR look for AP Index 11_12.xls
for MC look for MC_Index.xls - Daren Starnes
Resources
 Textbook Correlation:
Section 2.1 (pages 83 - 104)
 Most of the PowerPoint slides on the Instructor's
CD are very helpful.
 Use resources at
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.
html
 Monitor the AP Statistics List Serve [see Electronic
Discussion Groups on
http://apcentral.collegeboard.com/apc/public/course
s/teachers_corner/2151.html ] soon to be an AP
community see
https://epl.collegeboard.org/epl/login.do
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 2: Modeling Distributions of Data
Sample Formative Assessment Tasks
Skill-based tasks



Problem Tasks
CHECK YOUR UNDERSTANDING (textbook pages 89, 91,
97-98, and 103)
Use assessments at http://www.stats4stem.org/

Use Released Multiple Choice questions (see the last Suggested
Instructional Strategy above for a link to the list of MC questions) The
column "% correct " shows the global performance on the AP Exam
for that question. Add a column to the spreadsheet to keep a record of
the questions you used and when used.

Students in groups should discuss and write down the solution of an AP
Exam Free Response question, then compare it to the model solution,
and [selected group(s)] should present their solutions to the class
describing what they learned from their discussions
See the last Suggested Instructional Strategy above for a list of released
free response questions you can use (Do not use 2006 #1 until the end of
Chapter 1.) Add a column to the spreadsheet to keep a record of the
questions you used and when used.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 2: Modeling Distributions of Data
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variables (S-ID)
Standards
S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets
for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
NCSCOS http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
NCSCOS 1.01 Summarize distributions of univariate data by determining and interpreting measures of center, spread, position,…
NCSCOS 1.02 Analyze distribution of continuous univariate data (both normal and non-normal)
NCSCOS 3.06 Use normal distributions as a model for distribution. a. Investigate the properties of the normal distribution. b. Use the table of standard normal
distribution (Z)
AP Stats IIIC The normal distribution - Properties of the normal distribution, using tables of normal distribution, as a model for measurements
Concepts and Skills to Master (on paper and with technology)


the 68 – 95 – 99.7 rule
the standard normal distribution
Section 2.2 [Describing quantitative data with numbers]
 normal distribution calculations
 assessing normality
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Previous Skills and concepts in this course from Chapter 1 through Section 2.2
Academic Vocabulary
Empirical rule (68-95-99.7), Normal Curve, Normal Distribution, Normal Probability (Quantile) plot, Standard normal distribution, Standard
normal table (Table A)
Suggested Instructional Strategies
 Rely on the Teachers' Edition and the Platinum Resource Binder
 The text is excellent and students should have their book (and their calculator) at
each class. The challenge is how to inspire kids to read and study it. There should
be class discussions during each class using material from the book and using the
calculator. Consider assigning the next class' material as a prereading. Especially
focus on the boxes labeled "AP Exam Common Error" in the margins (and also in
Appendix A)
 With all students on their calculators and you on your projection calculator do
Technology Corners 2.2 on pages 118, 123, and 128 (or other Technology)
 Do the activity on page 111
Resources
 Textbook Correlation: Chapter 2 Section 2
(Pages 110 - 130)
 Most of the PowerPoint slides on the Instructor's CD are
very helpful.
 Use resources at
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.html
 Monitor the AP Statistics List Serve [see Electronic
Discussion Groups on
http://apcentral.collegeboard.com/apc/public/courses/teach
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 2: Modeling Distributions of Data
 Have a class discussion of Section 2.2's "Summary" on page 130
 The College Board has posted tremendously helpful material
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
 Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html, for FR look for AP
Index 11_12.xls and for MC look for MC_Index.xls - Daren Starnes
Sample Formative Assessment Tasks
Skill-based task
 CHECK YOUR UNDERSTANDING (textbook pages 114, 119 and
124 )
 Use assessments at http://www.stats4stem.org/
 Use Quizzes at http://bcs.whfreeman.com/tps4e/#628644__630756__
 Do the Chapter 2 AP Statistics Practice Test on page 138


Use ARTIST SCALE - Normal Distribution
http://ore.gen.umn.edu/artist/tests/index.html
Use Released Multiple Choice questions (see the last Suggested
Instructional Strategy above for a link to the list of MC questions) The
column "% correct " shows the global performance on the AP Exam
for that question. Add a column to the spreadsheet to keep a record of
the questions you used and when used.
ers_corner/2151.html ] soon to be an AP community see
https://epl.collegeboard.org/epl/login.do
Problem Task
At the End of Unit 2 do FRAPPY #2 [which uses 2003 #3]:
http://apstatsmonkey.com/StatsMonkey/FRAPPYs_files/Frappy2.pdf
(Or as an alternate, see the last Suggested Instructional Strategy above for a list of
free response questions that you could alternately use as your FRAPPY. Go to
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html for the FR
questions. Look for the link AP Index 11_12.xls. Add a column to the spreadsheet
and keep a record of the questions you used and when used.)
To Use Frappies: On the first page at
http://apstatsmonkey.com/StatsMonkey/FRAPPYs.html click on the FRAPPY
Presentation to learn about them and how to use them as Formative Assessments.
(Click on the Frappy Presentation to Advance to a new slide. You may also
download handout notes using the link to the right)
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.