AP Statistics Proposed Syllabus
COURSE DESCRIPTION:
AP Statistics is the high school equivalent of a one semester, introductory college statistics
course. In this course, students develop strategies for collecting, organizing, analyzing, and
drawing conclusions from data. Students design, administer, and tabulate results from surveys
and experiments. Probability and simulations aid students in constructing models for chance
behavior. Sampling distributions provide the logical structure for confidence intervals and
hypothesis tests. Students use a TI-83/84 graphing calculator or a TI Nspire, Fathom, statistical
software with a selection of statistics activities, and Web-based java applets to investigate statistical concepts. The teacher has a SmartBoard and TI SmartView, TI Nspire software, and Fathom to use for demonstration purposes and to instruct students how to use the different forms of technology. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.
COURSE GOALS:
In AP Statistics, students are expected to learn
Skills
• To produce convincing oral and written statistical arguments, using appropriate
terminology, in a variety of applied settings.
• When and how to use technology to aid them in solving statistical problems
Knowledge
• Essential techniques for producing data (surveys, experiments, observational studies),
analyzing data (graphical & numerical summaries), modeling data (probability, random
variables, sampling distributions), and drawing conclusions from data (inference
procedures – confidence intervals and significance tests)
Habits of mind
• To become critical consumers of published statistical results by heightening their
awareness of ways in which statistics can be improperly used to mislead, confuse, or
distort the truth.
Course Materials
Primary Text
TPS4 - Starnes, Yates and Moore. The Practice of Statistics, Fourth Edition. New York, NY: W H Freeman and Company, 2012. ISBN 978-1-4292-6258-3.
References, Resource Materials and Their Labels
BVD - Bock, Velleman and DeVeaux. Stats Modeling the World, Second Edition(AP Edition). Boston, MA: Pearson Education, Inc., 2007.
TPS- TTR - Tabor and Brown. The Practice of Statistics, Fourth Edition. Teacher’s Titanium Resource Binder. New York, NY: W H Freeman and Company, 2011.
CBWH - CollegeBoard. AP Statistics, Workshop Handbook, 2011-2012.
ABS - Scheaffer, Gnandesikan, Watkins and Witmer. Activity-Based Statistics. New York, NY: Springer – Verlag, 1996.
WKST - Rossman, Chance and Oehsen. Workshop Statistics: Discovery with Data and the Graphing Calculator, Third Edition. Hoboken, NJ: John Wiley & Sons, Inc., 2008.
TPS – FG - Erickson, Tim. The Fathom Guide for The Practice of Statistics, Third Edition. New York, NY: W H Freeman and Company, 2008.
Spiegel and Stephens. Statistics, Fourth Edition. New York, NY: McGraw-Hill, 2011.
TPS3 -Yates, Moore & Starnes. The Practice of Statistics, 3d edition, W.H. Freeman, 2006.
TPS2 - Yates, Moore & Starnes. The Practice of Statistics, 2nd edition, W.H. Freeman, 2003.
KL-APSO - Kucera, Lee. Instuctor for the Course: Y2984: Teaching AP* Statistics (Online) X 394.18 (Summer 2012). Notes, activities and other instructional materials.
APP - Internet applets on various university and other sites.
F - Fathom, Release 2. Key Curriculum Press, Berkeley, CA.
NB3R - Curriculum List/Guide to all NUMB3Rs episodes complete with TI Worksheets and Activities.
TI-83+, TI-84, TI-84+ graphing calculators and Graph View Software.
TI Nspire CAS Teacher Software
Timeline for Fall Semester/Spring Semester
Both semesters are based upon 55 minute class sessions. Because classes are taught on a college schedule, AP Statistics will only meet class sessions Monday, Wednesday and Friday. This breaks down into 50 sessions per semester. Every weekday evening, except Friday, tutorials are held from 7-9pm. I intend to schedule review sessions for Midterms/Finals and AP review during evening tutorials to make up time needed.
11 | Page
SEMESTER 1Chapter / Class Sessions
1 / 9
2 / 7
3 / 8
4 / 11
5 / 8
6 / 9
Midterms/Finals / 5
SEMESTER 2
Chapter / Class Sessions
7 / 7
8 / 7
9 / 8
10 / 8
11 / 6
12 / 7
Review for AP / 10
TOTAL / 110
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COURSE OUTLINE Students will gain proficiency on accuracy and communication of statistical concepts throughout the course, to include effectively communicating how methods, results and interpretations of data for any given experiment are valid. They will learn that writing complete responses using appropriate justifications is a critical aspect of gaining statistical proficiency. Also, graphical displays and other statistical analysis will be documented when using Fathom and/or graphing calculators. Homework will be assigned for each section covered in the textbook. Activities and projects are assigned throughout the course. Both are assigned to develop effective statistical-communication skills, where students are required to prepare frequent written and oral analyses of real data. In the “Day” column, projects will be labeled with P, technology with Tech, activities with ACT. Supplemental materials will be labeled with identifying initials and listed in either Topics/Activities column or Objectives Column. Exercises with an R as a superscript are problems that review material from previous chapters.
Chapter 1
Day / Topics/Activities / Objectives: Students will be able to… / AP Course Obj/ Homework in text1
ACT / Chapter 1 Introduction
Activity: Water, Water Everywhere! TPS- TTR
This is a great alternate Activity to introduce the major themes of the AP Statistics course. Students will collect data, perform a simulation, and make a conclusion based on their results.
Mr. Starnes’s Infamous AP Statistics Survey TPS- TTR
This will be used to gather data about my students that can used all year long. / · Identify the individuals and variables in a set of data.
· Classify variables as categorical or quantitative. Identify units of measurement for a quantitative variable. / I. Exploring data: describing patterns and departures from patterns.
1, 3, 5, 7, 8
Tech / Students will be given copies of the Handout, “Calculator Functions for Statistics,” which is a 6 page document. An excerpt from the handout follows:
2 / 1.1 Bar Graphs and Pie Charts, Graphs: Good and Bad
KL-APSO - Nice video to introduce stats.
http://www.youtube.com/watch?v=JS9GmU5hr5w / · Make a bar graph of the distribution of a categorical variable or, in general, to compare related quantities.
· Recognize when a pie chart can and cannot be used.
· Identify what makes some graphs deceptive. / IE1 – Frequency tables and bar charts
IE4 – Comparing distributions using bar charts
11, 13, 15, 17
3
Tech / 1.1 Two-Way Tables and Marginal Distributions, Relationships Between Categorical Variables: Conditional Distributions, Organizing a Statistical Problem.
TPS – FG A version of the Fathom activities, “Describing Distributions with Graphs” and “Describing Distributions with Numbers” will be assigned to introduce students to Fathom and to support objectives. / · From a two-way table of counts, answer questions involving marginal and conditional distributions.
· Describe the relationship between two categorical variables by computing appropriate conditional distributions.
· Construct bar graphs to display the relationship between two categorical variables. / IA1 – 4 - Center and Spread, clusters and gaps; outliers and unusual features; shape.
19, 21, 23, 25, 27-32
4 / 1.2 Dotplots, Describing Shape, Comparing Distributions, Stemplots
KL-APSO 1.1s: Categorical Graphs, Stem-and-Leaf Plots and Dotplots / · Make a dotplot or stemplot to display small sets of data.
· Describe the overall pattern (shape, center, spread) of a distribution and identify any major departures from the pattern (like outliers).
· Identify the shape of a distribution from a dotplot, stemplot, or histogram as roughly symmetric or skewed. Identify the number of modes. / 37, 39, 41, 43, 45, 47
IB1-5 –
Summarizing distributions of univariate data
1. Measuring center: median, mean
2. Measuring spread: range. interquartile range, standard deviation
53, 55, 57, 59, 60, 69-74
3. Measuring position: quartiles, percentiles, standardized scores (z-scores)
4. Using boxplots
79, 81, 83, 87, 89
5. The effect of changing units on summary measures
91, 93, 95, 97, 103, 105, 107-110
5
Tech / 1.2 Histograms, Using Histograms Wisely
Students will be taught how to use the TI-84 Plus graphing calculator to construct histograms. / · Make a histogram with a reasonable choice of classes.
· Identify the shape of a distribution from a dotplot, stemplot, or histogram as roughly symmetric or skewed. Identify the number of modes.
· Interpret histograms.
6
Tech / 1.3 Measuring Center: Mean and Median, Comparing Mean and Median, Measuring Spread: IQR, Identifying Outliers
Students will be taught how to use the TI-84 Plus graphing calculator to find measures of center. / · Calculate and interpret measures of center (mean, median)
· Calculate and interpret measures of spread (IQR)
· Identify outliers using the 1.5 ´ IQR rule.
7
Tech / 1.3 Five Number Summary and Boxplots, Measuring Spread: Standard Deviation, Choosing Measures of Center and Spread
Students will be taught how to use the TI-84 Plus graphing calculator to draw boxplots, find 5-point summary, standard deviation and outliers. / · Make a boxplot.
· Calculate and interpret measures of spread (standard deviation)
· Select appropriate measures of center and spread
· Use appropriate graphs and numerical summaries to compare distributions of quantitative variables.
8
ACT / Chapter 1 Review KL-APSO The Great Reese’s Minis Experiment (Great review activity!)
Chapter 1 Review Exercises
9 / Chapter 1 Test
P / Chapter 1 Project: Critical statistical analysis – each student collects data and analyzes it using the techniques learned in this unit and prepares a written analysis. Evaluation will use a four-point rubric like the AP Free Response questions. There are many data sets to choose from with KL-APSO WKST, Fathom folder, and internet.
Chapter 2
Day / Topics/Activities / Objectives: Students will be able to… / AP Course Obj/ Homework in textACT
1 / Is this normal? (my own marble rolling simulation lesson) Students submit their own group graph and class graph, identify measures of center and write statements of comparison.
2.1 Introduction, Measuring Position: Percentiles, Cumulative Relative Frequency Graphs, Measuring Position: z-scores
KL-APSO – 1.5s z-scores / · Use percentiles to locate individual values within distributions of data.
· Interpret a cumulative relative frequency graph.
· Find the standardized value (z-score) of an observation. Interpret z-scores in context. / I & III-C1
C. The normal distribution
1. Properties of the normal distribution
IB3 3. Measuring position: quartiles, percentiles, standardized scores (z-scores)
5, 7, 9, 11, 13, 15
2 / 2.1 Transforming Data, Density Curves
KL-APSO – 1.6s – Univariate Transformation / · Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.
· Approximately locate the median (equal-areas point) and the mean (balance point) on a density curve. / 19, 21, 23, 31, 33-38
IB5
5. The effect of changing units on summary measures
3
NB3R
Tech / 2.2 Normal Distributions, The 68-95-99.7 Rule, The Standard Normal Distribution
episode #: 316 "Contenders" Weighted Averages, Z-scores
Technology: Standard
Normal Curve Calculations with the Calculator and with an Applet / · Use the 68–95–99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points one, two, or three standard deviations on either side of the mean.
· Use the standard Normal distribution to calculate the proportion of values in a specified interval.
· Use the standard Normal distribution to determine a z-score from a percentile. / 41, 43, 45, 47, 49, 51
4
Tech / 2.2 Normal Distribution Calculations
Technology: Normal Curve
Calculations with the Calculator and with an Applet / · Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile. / IIIC -
2. Using tables of the normal distribution
3. The normal distribution as a model for measurements
53, 55, 57, 59
5
Tech / 2.2 Assessing Normality
Normal Probability Plots on the Calculator / · Make an appropriate graph to determine if a distribution is bell-shaped.
· Use the 68-95-99.7 rule to assess Normality of a data set.
· Interpret a Normal probability plot / 63, 65, 66, 68, 69-74
6 / Chapter 2 Review Chapter 2 Review Exercises
7 / Chapter 2 Test / 39R, 40R, 75R, 76R
Chapter 3
Day / Topics / Objectives: Students will be able to … / AP Course Obj1
ACT / Chapter 3 Introduction
TPS- TTR
Activity: CSI Stats: The Case of the Missing Cookies
3.1 Explanatory and response variables
3.1 Displaying relationships: scatterplots
3.1 Interpreting scatterplots
Technology:
Scatterplots on the Calculator / · Describe why it is important to investigate relationships between variables.
· Identify explanatory and response variables in situations where one variable helps to explain or influences the other.
· Make a scatterplot to display the relationship between two quantitative variables.
· Describe the direction, form, and strength of the overall pattern of a scatterplot.
· Recognize outliers in a scatterplot. / D. Exploring bivariate data
1. Analyzing patterns in scatterplots
1, 5, 7, 11, 13
2. Correlation and linearity
14–18, 21, 26
3. Least-squares regression line
27–32, 35, 37, 39, 41
4. Residual plots, outliers and influential points
43, 45, 47, 53
49, 54, 56, 58–61
63, 65, 68, 69, 71–78
2
Tech / 3.1 Measuring linear association: correlation
3.1 Facts about correlation
Technology: Correlation
and Regression Applet / · Know the basic properties of correlation.
· Calculate and interpret correlation.
· Explain how the correlation r is influenced by extreme observations.
3
Tech / 3.2 Least-squares regression
3.2 Interpreting a regression line
3.2 Prediction
Technology: Least-Squares Regression Lines on the
Calculator / · Interpret the slope and y intercept of a least-squares regression line.
· Use the least-squares regression line to predict y for a given x.
· Explain the dangers of extrapolation.
4
NB3R
Tech / 3.2 Residuals and the least-squares regression line
3.2 Calculating the equation of the least-squares regression line
episode #: 308 "Hardball"
Least Squares Regression
Technology: Residual Plots and s on the Calculator / · Calculate and interpret residuals.
· Explain the concept of least squares.
· Use technology to find a least-squares regression line.
· Find the slope and intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation.
5 / 3.2 How well the line fits the data: residual plots
3.2 How well the line fits the data: the role of r2 in regression / · Construct and interpret residual plots to assess if a linear model is appropriate.
· Use the standard deviation of the residuals to assess how well the line fits the data.
· Use r2 to assess how well the line fits the data.
6 / 3.2 Interpreting computer regression output
3.2 Correlation and regression wisdom / · Identify the equation of a least-squares regression line from computer output.
· Explain why association doesn’t imply causation.
· Recognize how the slope, y intercept, standard deviation of the residuals, and r2 are influenced by extreme observations.
7
P
F
Tech / Chapter 3 Review Chapter 3 Review Exercises
Project: Pinching Pages Fathom activity which has students collect data, create a line of best fit using a visual of the “least squares” on regression line, determine residuals, write conclusions and make predictions. Evaluation will use a four-point rubric like the AP Free Response questions.
8 / Chapter 3 Test / Least Squares Regression / 33R, 34R, 79R, 80R, 81R
Chapter 4