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Frivolous & Fun Stuff

Probabilities in Monopoly®

 

TED talks:

Spanish with English subtitles, Eduardo Sáenz de Cabezón: Math is forever.

Roger Antonsen: Math is the hidden secret to understanding the world

Salman Khan (the Khan Acadamy guy):  Let's use video to reinvent education

 

Youtube videos:

Malcolm Gladwell on the importance of stubbornness (27:37)

Rethinking Education – Sal Khan (1:30:08)

 

CBC Radio, How big data is changing the video you watch (10:25)

Malcolm Gladwell podcast, Revisionist History

 

Download

[Flatland (the book) can be downloaded from Wikipedia]

Download Fathom for Windows from our Google Classroom (only available to AP Statistics students).  Fathom for the Mac is NOT FREE.

Download Mr. Shim’s recommended Graphing Software (free!)

Grade 9 Academic EQAO Formula Sheet

Geometer Sketchpad 5.06 (download)

License name:  ONTARIO DSBYORK

Authorization code:  KQJ9P1RF7C9CVGP1M7REVX58

 

 

Math Tools & Resources

Desmos Graphing Tool (online version)

Math Tools (click here)

Probability Tools (click here)

Vector Visualizer (try this online vector tool for visualizing)

Wheel Decide practice function spinners: function; a & k coeffcients; p & q coefficients

Wheel Decide practice trig spinners:  a & k coeffcients; p coefficient (radians);  q coefficient

 

UWaterloo CEMC Courseware – on line instructional videos with exercise & enrichment questions (a work in progress, but an excellent resource for 12U Advanced Functions and 12U Calculus & Vectors)

Grade 12 AP Statistics

·         Hey, our textbook Stats: Modeling the World, is available online!

·         Download the TI-83 Plus guidebook PDF from Texas Instruments

·         Graphing/Charting and General Data Visualization App

·         Normal Distribution calculator, by David Lane

 

Date

Topics & Learning Goals

Resources & Work

Feb 4

Ch. 1.  Read it. This is going to be fun.

Ch. 2 – Categorical vs Quantitative

Know that the Who, What, Why, Where, When and how of the data help us understand the context.

Understand the terms data, case, population, sample, variable, units, categorical variable, and quantitative variable.

Recognize the difference between categorical and quantitative variables.

Online survey sent to everyone’s GApps email.

Read Chapter 1 Text p.2 – 6…it’s an entertaining read!

Text: p.7 – 14

p.16 #3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

 

Optional:

YouTuber, Ben Lewis teaches AP Statistics.  He is also teaching chapter by chapter using the same textbook.

5

Lunar New Year

Ch. 3 – Displaying and Describing Categorical Data

Be able to recognize when a variable is categorical and choose an appropriate display for it (frequency table, bar chart or pie chart. 

Understand how to examine the association between categorical variables by comparing conditional and marginal percentages on a contingency table.

*Understand Simpson’s paradox

Handout, Ch. 3 Displaying & Describing Categorical Data  (Check here for completed notes.)

Text p.20 – 37

Acquire and install Fathom software for Windows only.

p.38 #5, 7, 9, 11, 15, 19, 21, 25, 27, 29, 31, 33, 39

 

Optional:

Mr. Nystrom, APStatsGuy, contingency tables  (13:35)

Mr. Nystrom, APStatsGuy, independence vs. association  (8:42)

6

Ch. 4 – Displaying Quantitative Data

Understand how to create histograms, stem & leaf plots and dot plots.

Describe a distribution by it’s shape (modes, symmetrical, gaps and outliers), center (mean vs median) and spread (range, IQR, standard deviation).

Explore the software Fathom.

Handout, Ch. 4  Mean and Standard Deviation  (Check here for completed notes.)

Handout, Ch. 4  Median & Quartiles  (Check here for completed notes.)

Text p.44 – 71

p.72 #5, 9, 11, 13, 15, 21, 23, 29, 33, 37, 41, 43, 49

(we will re-do the bolded questions tomorrow, using Fathom & the TI-84s)

 

CANCELED – Immunization clinic in our classroom.  Class today will be in room 2027.

7

AMC; Report Cards; Grad retake day

Work Period

Let’s have a discussion about Data Visualization.

 

Ch. 4 using Fathom and TI

 

 

Handout, Fathom Quick Reference

Mandatory: watch the video of Hans Rosling at TED2006, “The best stats you've ever seen”. (~20 min)

Re-do using Fathom, p.72 #13, 15, 33, 37, 41

 

Optional:

Hans Rosling at TEDIndia2009, “Asia's rise — how and when”. (15:50)

Hans Rosling at TED2010, “Global population growth, box by box”. (10:04)

8

Ch. 5 – Comparing Distributions

Understand how to create a box-plot (5 number summary, outliers, percentiles).

Compare sets of data using histograms and box-plots

*Transform data to make it more symmetrical.

Text p.80 – 93

p.95 #5, 9, 11, 15, 21, 23, 29, 33 (on Fathom), 35, 37, 39

11

Ch. 6 – Standard Deviation and Z-Scores

Know how to calculate z-scores.

Understand and apply the properties of a normal distribution.

*Construct a Normal Probability Plot

Text p.104 – 127

Good examples on p.122 & 123

 

p.129 #1, 5, 7, 9, 13, 17, 19, 21, 29, 31, 39, 45, 47

12

Work Period

Ch. 3—6 assignment  

Partners and questions are posted on the Google Classroom.

13

Ch. 7 – Scatterplots & Correlation

Describe the relationship between two variables using a scatterplot by discussing direction, form, strength and the effect of outliers.

*Calculate the correlation coefficient using  and using TI calculator

Understand when it is appropriate to use r.

Understand correlation does not imply causation.

Understand the effect of lurking variables.

*Know some ways to straighten a scatterplot.

*Understand differences between correlation & association.

Text p.146 - 162

p.164 #1, 5, 11, 15, 17, 21, 25, 29, 37

Do #33 & 41 using Fathom.

14

Work Period

Immunization clinic in our classroom.  Class today will be in room 2027.

15

Ch. 8 – Linear Regression (part 1)

*Calculate the least squares line of best fit based on z-scores , and based in real units,   where  and .

Be able to interpret the slope and y intercept of the regression line in context.

Text p.179 – 192

p.192 #1, 3, 5, 7, 9, 11, 13

18

Family Day

 

19

Practice using TI-83s

TI Tips on pages:  15*, 46, 65*, 86, 117*, 119*, 125.

Items marked with an * are the most important to know.

Quiz Chapters 2 - 6

20

Ch. 8 – Linear Regression (part 2)

*Connection between r(the correlation coefficient) and R2 (the variability accounted for, association).

*Calculate the residuals, and create a residual plot.

*Calculate the standard deviation of the residuals using .

*Interpret the results of the residual plot and standard deviation of the residuals.

p.192 #23, 27, 29, 31, 37, 39, 45, 47, 51 (#51 has been entered into Fathom.  Check the Google classroom to download.)

Box on top of p.183 is important.

 

21

Work Period

 

22

Ch. 9 – Non-Linear Regression

Understand the following terms:  extrapolation, outliers

*Leverage – difference between x and the mean of x.

*Residual – difference between the actual value of y and the predicted value of y.

*Influential point – a point that changes the model significantly

Understand the effect of lurking variables (again).

*Regressions based on summary statistics.

Text p.201 – 212

 

Using Fathom features:

·         Copy As Picture

·         Scatter Plot

·         Line of Best Fit

·         Show Squares

·         Make a Residual Plot

·         Using sliders

·         Create a Non-linear model

Handout, Regression with Fathom; download the required files here.

p.214 #1, 5, 7, 9, 11, 17, 21, 23, 29

25

Work period

 

26

PCF

Ch. 10 – Re-expressing Data

*Know the 4 Goals of Re-expression:

Make the distribution more symmetric

Make the spread of several groups more alike

Make the form of a scatter plot more linear

Make the scatter plot more evenly spread out rather than thickening at one end.

*Know how to pick a type of re-expression based on the “Ladder of Powers”

*Re-expressing data using the TI calculator

Text p.222 – 236

 

re-expressing data

 

Good example on p.232 for the TI

Using the TI calc

 

p.239 #1, 3, 5, 7, 9, 15 (use TI), 17 (use TI), 27, 29

27

Statistical Analysis Assignment

Work period

 

28

Statistical Analysis Assignment

Work period

 

March 1

Statistical Analysis Assignment

Work period

 

4

Ch. 11 – Understanding Randomness

Creating a simulation using random number generators

Text p. 256 – 263

p.265 #11, 13, 15, 19, 25, 33, 39

5

Work period

 

6

Ch. 12 – Surveys

Understand the meaning and importance of the terms:  population, sample, sampling frame, survey, bias, randomness, sample size, census, population parameter vs sample statistic

Know different kinds of sampling techniques:  Simple Random Sample, Stratified (strata = homogeneous), Cluster (cluster = heterogeneous), Multistage, Systematic, Voluntary Response, Convenience

Tips on creating a valid survey

Know different kinds of bias:  Response Bias, Non-Response Bias, Sampling Bias (Undercoverage Bias)

Text p.268 – 285

(beware of the creepy guy on p.268)

Literary Digest Poll

 

Strange analogy on p.276 involving Boston Cream Pie

 

strange video on response bias

p.288 #1, 3, 5, 9, 13, 17, 19, 23, 25, 33

7

Review – Chapters 2 – 7

Review – Chapters 8 – 12

 

8

Ch. 13 – Experiments

Observational study:  retrospective and prospective

Experimental study:  Subjects are randomly assigned to a treatment which must have at least one explanatory variable (factor) to manipulate at least one response variable. 

The 4 Principles of Experimental Design:  Control, Randomize, Replicate, Block

Statistically significant, control treatments, blind experiments, placebo effect, randomized block design, matching, randomized two-factor experiment, lurking vs confounding

Text p.292 – p.309

 

Experimental Design

 

Double-Blind Experiment (you tube link)

 

Results of violin experiment (link to pdf)

p.313 #1, 3, 5, 7, 11, 17, 27, 29, 33, 35

11 – 15

March Break

 

18

Ch. 14 – Probability Basics

Understand the meanings of:  trial, outcome, event, sample space, empirical vs theoretical vs subjective probability, independent events

*The Law of Large Numbers

Basic Rules of Probability

1.      

2.       The sum of all possible probabilities of an event is 1.

3.        (complement rule)

4.        for mutually exclusive events.

5.      

Text p.324 – 336

 

Click below to look at the origins of probability Problem of Points

p.338 #1, 7, 11, 19, 21, 23, 29, 33, 35, 41, 43

 

 

19

Statistics Test (Chapters 2 – 12)

 

20

Ch. 15 – Probability Rules

1.        for any pair of events.

2.       Conditional Probability: 

Also know tests for independence and how to use tree diagrams

Text p.342 - 360

p.361#1, 3, 7, 9, 13, 15, 17, 19, 21, 27, 31, 37, 39, 45

21

Naw Ruz (Ismaili)

Ch. 16 – Mean & Variance

Be able to recognize the difference between a discrete random variable and a continuous random variable.

Recognize that the expected value of a random variable X, is equivalent to the population mean, µ.

*Calculate the standard deviation of a random variable X using

*Apply the following properties for expectation and variance for two independent variables X and Y. 

                           

                                

              

Text p.366 – 382

p.383 #1, 3, 5, 9, 11, 13, 19, 21, 25, 27, 33, 35, 37, 43

22

Interim  Report Cards

Ch. 17 – Probability Models

Recognize the difference between a geometric (models a waiting time) and a binomial probability model (models # of successes).

Understand the term “Bernoulli Trial”.

Geometric:              

Binomial:   ,  ,

Using the Normal Model to approximate a Binomial Model.

Text p.388 – 400

p.401 #1, 9, 11, 15, 17, 19, 21, 23, 27, 31, 35

 

Solutions to Chapter 17

25

Other probability models:  Hypergeometric and Uniform.

Chapter 7 from the old MDM4U textbook is called “Probability Distributions”. Check the AP Stats Team Drive, in a folder called “MDM textbook”.

The answers to homework questions is a separate file called, “Answers”.

7.4 Hyper Geo Dist,  p.404 #1, 3, 4, 6, 7, 9 – 12

Ch.7 Review, p.406 #1, 2, 4

Solutions to handout

26

 

Review questions:  p.405 #1, 3, 7, 9, 15, 17, 23, 31, 35, 41

Review solutions

27

OSSLT (school is open for Grade 10s, but we don’t have class)

 

28

Parents Night

Review for Test 2

 

29

Ch. 18 – Sampling Distribution Models

*Central Limit Theorem – conditions for using CLT

Sampling Distribution Model for a proportion is

Sampling Distribution Model for a Mean is

p.412 – p.430

In the data text book, you can find this topic in section 8.6

Mr.Nystrom video

Central Limit Theorem

CLT simulation

p.432 #1, 3, 5, 7, 9, 15, 21, 23, 29, 31, 37, 39, 43, 45

April 1

Test 2:  Chapters 14 – 17 and Hypergeometric, Uniform Distributions

 

April 2

Ch. 19 - Confidence Intervals for Proportions

Creating & interpreting CI’s for proportions:

Calculating the margin of error,  based on a given CI. 

Calculating the sample size, n, based on a given CI.

p.439 – p.453

 

In the data text book, you can find this topic in section 8.6

 

Confidence intervals video

 

In class, 3-sided coins.  Estimate the probability of tossing “sides”.

p.455 #1, 5, 7, 9, 13, 17, 23, 27, 29, 31

3

Euclid

Work period

 

4

Ch. 20 – Hypothesis Testing for Proportions

Understand the setup, mechanics and conclusion for a hypothesis test

*Understand when and how to do a two-sided hypothesis test. 

p.459 – 479

For two tail tests, see example on p.466

p.476 #3, 5, 9, 13, 17, 19, 21, 25, 29

#13 and #21 require doing a two tail test.

5

Constructing Simulations using Excel and Fathom

 

8

Work period

 

9

*Ch. 21 – More about Tests and Intervals

Understanding how to conclude a hypothesis test by either saying “reject H0”, or “fail to reject H0”.

 

Type I and Type II errors and how to reduce them

Understand what the Power of a Test means

p.480 – 497

 

Type I and Type II errors

Type I and Type II errors and the power of a test

p.499 #3, 7, 9, 15, 17, 21, 25, 27, 29, 33

10

FGH

Work period

Get to know your calculator (again!)…here are some TI Tips that you should familiarize yourself with: 

p.448, p.469, p.510, p.515

11

*Ch. 22 – Comparing Proportions

Know the sampling distribution model for the difference between two proportions (box on p.507)

Know how to create and interpret a confidence interval for the difference between two proportions (box on p.508)

Know how to perform a two proportion hypothesis test and interpret the results (box on p.513)

p.504 – 518

 

Hypothesis Testing comparing Proportions video

 

Confidence Intervals for comparing proportions

 

p.519 #3, 5, 9, 11, 17, 19, 23, 25, 31

12

FGH

Work period

 

15

*Ch. 23 – Inferences about Means

Reminder of the CLT for means  

For smaller samples, use the students’s t (Gosset’s t) instead of a z-score.

Know how to create and interpret a confidence interval for a mean (box on p.523)

Know how to perform a hypothesis test a mean and interpret the results (box on p.543)

p.530 - 550

Confidence Intervals for Means

 

z-score vs t-score

 

example of a two tail test for a mean

 

**You will need to know how to calculate the probabilities based on t values using your TI-83, as the text book does not provide a t table. (see the TI Tip on p.545)

p.554 #1, 3, 5, 7, 9, 11, 19, 21, 25, 29, 31, 37

16

Work period

 

17

*Ch. 24 – Comparing Means

Know the sampling distribution model for the difference between two means (box on p.563)

Know how to create and interpret a confidence interval for the difference between two means (box on p.564)

Know how to perform a two sample hypothesis test for the difference between two means and interpret the results (box on p.569)

 

Note that you do NOT need to know the material on The Pooled t-Test starting on page 574.

p.560 - 574

Difference of Means

 

 

**You will need to know how to calculate the degrees of freedom using the TI-83.  Check out the TI-Tip starting at the bottom of page 567.

p.579 #1, 5,7, 9, 13, 17, 19, 21, 23, 27, 33, 35

18

Work period

 

19

Good Friday

 

22

Easter Monday

 

23

*Ch. 25 – Paired Samples and Blocks

(Comparing Means for groups that have data that are NOT independent)

 

Understand circumstances that could lead to paired (dependent) data:

1) Blocked pairs compare data before and  after an experiment

2) Matched pairs are data from an observational study

 

Understand the Assumptions and Conditions (p.589)

Know how to create and interpret a confidence interval for the difference between two means of paired data (box on p.595)

Know how to perform a two sample hypothesis test for the difference between two means of paired data and interpret the results (box on p.591)

p.587 – 600

How to create null and alternate hypotheses review

p.602 #1, 3, 5, 9, 11, 13, 17, 19, 23, 25

24

Work period

 

25 Full Disclosure

*Ch. 26 – Chi-Squared Distribution

The chi-square statistic is .  It is used for the following tests:

Chi-squared goodness of fit test (p.622, 623). This is testing to see if a model is appropriate for the data.

Chi-squared test of homogeneity (p.627).  This is like the z-test for two proportions.

Chi-squared test for independence(p.633)

p.618 – 640

Notes:  You won’t be able to use your TI for the TI tip on page 624.  This is only for the TI-84s.  You can, however, do the cumulative distribution function on your TI-83.

Goodness of Fit

Homogeneity

Independence

p.642 #1, 3, 7, 11, 13, 15, 17, 19, 23, 29, 35

26 Holy Friday

Work period

 

29

*Ch. 27 – Inferences for Regression

The idealized line of best fit is denoted .  This corresponds to our fitted line .

Assumptions & Conditions:

1. Linearity

2. Independence

3. Equal Variance

4. Normal Population

Sampling Distribution for Regression Slopes (bottom of p.658)

p.649 – 665

Notes:  The material after page 665 is all optional. 

p.673 #1, 3, 5, 13, 15, 23, 25, 27, 33, 41

30

Work period

 

May 1

 

 

2

Prom; CEMC marking

 

 

3

CEMC marking

PA Day

 

6

Ramadan begins

 

 

7

Review for test

 

8

Test – Statistical Inference (chapters 18 – 25)

 

9

Review for AP Exam

 

10

Review (Multiple Choice)

 

Link to information regarding the  AP Exam

13

Review  (Full response – short answer)

Link to 2012 practice exam

14

Review (Full response –big answer)

 

15

Review (Full response –big answer) Day 2

 

16

AP Statistics Exam, 12:00 noon

 

17

4.1 Organized Counting

Understand the Fundamental Counting Principle; when to correctly multiply or add (and sometimes subtract).

Using “Counting Boxes” with annotations for proper solutions.

 

4.2 Factorials and Permutations

Understand the basics of combinatorics including factorial and permutation notation.

Learn and practice how to communicate your solution.

Handout, 4.1 Intro to Organized Counting  (Check the completed notes here.)

Handout, 4.2 Factorials and Permutations  (Check the completed notes here.)

§4.1  p.229 # 1–5, 8–10, 13, 14, 17, 18ab

§4.2  p.239 #1 – 4, 6, 7, 10, 15, 17, 18 , 11,   13, 14, 19, 22, 16, 12

20

Victoria Day

 

21

Work period

Handout, Permutations with Restrictions  (Check the completed notes here.)

§4.1  p.230 #19, 23, 24

§4.2  p.239 #9, 11, 12, 16, 20, 22, 23

22

4.3 Permutations with some identical items

Understand how to calculate the number of permutations of n objects where some of the objects are identical.

Handout, 4.3 Arrangements with Some Alike  (Check the completed notes here.)

(If you want, start tomorrow’s homework.  Today’s homework is a bit light.)

§4.3  p.245 #2–7, 10, 12, 14, 16

23

Work period

Handout, Permutations - Extra Problems

24

Dice Assignment 1

 

27

5.1 Venn Diagrams

5.2 Intro to Combinations 

Understand how to solve problems using Venn Diagrams.  Learn the principal of inclusion and exclusion.  Recognize the difference between a permutation and a combination.  Solve problems involving combinations.

Handout, 5.1 Counting Using Venn Diagrams  (Check the completed notes here.)

 

Handout, 5.2 Introduction to Combinations  (Check the completed notes here.)

§5.1  p.270 #1–5, 9

§5.2  p.279 #1, 2, 4, 5, 9, 11, 12, 13, 18, 22

28

Work period

Handout, 5.2 Introduction to Combinations

Handout, p.4  #16

29

5.3 Types of Combinations

Solve problems with combinations involving different scenarios:  size of the subset is known / unknown and some items identical.

Handout, 5.3 Take ‘em or leave ‘em Counting  (Check the completed notes here.)

§5.3  p.286 #1 – 11, 14, 16, 18, 22, 24

30

Work period

Handout, Combinations & Permutations

31

Work period

Dice Assignment due

Combinatorics & probability

June 3

Dice Assignment II rolled out

Handout, Review Combinatorics Activity – Make up a Question

Chapters 6.1 – 6.5

4

Choose & arrange type questions

Work period

Handout, Review Probability

5

Eid-ul-Fitr

Work period

·         Gambling Case Study

·         Poker

·         Blackjack

·         Roulette

·         Lotteries

 

6

 

 

7

Carnival

 

Carnival Schedule: ??? (last year’s)

Period 1      8:50 - 9:30

Period 2      9:35 - 10:05

Period 3     10:10 - 10:45

Period 4     10:50 - 11:25

Period 5     11:30 - 12:05

The Carnival will run from 12:05 - 3:30

10

 

 

11

Test 4 – Combinatorics & Probability

 

12

Dice Assignment II due

 

13

 

 

14

Review for Exam

Final exam review

Read the sample Final Exam cover page.

Download and check the corrections for the MDM textbook.

17

Review for Exam

 

18

Detailed Exam Review

2.1 Graphs – be able to draw and interpret graphs

2.3 Sampling Techniques (note the vocabulary and the typical examples for different sampling techniques)

2.4 Bias

2.5 Measures of Central Tendencies  (mean & median)

2.6 Measures of Spread  (standard dev & quartiles)

3.1 scatter plots

3.2 linear regression

3.3 Non-Linear Regression (it is not reasonable to DO non-linear regression without a computer, but you should know how to discuss, interpret and explain non-linear regression.)

3.4 Cause & Effect (5 Types of Cause & Effect)

3.5 Critical Analysis (be able to interpret statistics)

4.1—4.3 Permutations

5.1—5.3 Combinations

6.1—6.5 Probability

7.1 Probability Distributions

7.2 Binomial Distributions (same as AP Stats)

7.3 Geometric Distributions (same as AP Stats; different format)

7.4 Hypergeometric Distributions (In AP Stats we always approx. using a normal dist. In Data Mgt the numbers are small and simple enough that we calculate and graph the actual distribution.)

8.1 Continuous Distributions (introduces “area under the curve =1” distributions, particularly Uniform.)

8.2—8.4 Normal Distributions (same as AP Stats BUT we only use the table on P606)

8.5 Hypothesis Tests (only 1-tail normal tests)

8.6 Confidence Intervals

19

Exams

 

20

Exams

 

21

Exams

 

24

Exams

 

25

Exams

 

26

Exam Feedback Day

 

8:50 – 9:20         Period 1

9:25 – 9:55         Period 2

10:00 – 10:30     Period 3

10:35 – 11:05     Period 4

11:10 – 11:40     Period 5

11:45 - 12:25      Lunch

27

Grad

PA Day

 

28

PA Day

 

Mon July 1st

Canada Day