# Frivolous & Fun Stuff

TED talks:

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

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

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

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

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

Authorization code:  KQJ9P1RF7C9CVGP1M7REVX58

# Math Tools & Resources

Desmos Graphing Tool (online version)

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)

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

·         Graphing/Charting and General Data Visualization App

·         Normal Distribution calculator, by David Lane

## 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.

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.

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.

Student Data Analysis Activity.  Check the Google Classroom post.

21

Work Period

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

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

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

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

27

Work period

28

Ch. 11 – Understanding Randomness

Creating a simulation using random number generators

Text p. 256 – 263

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

March 1

Work period

4

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)

Strange analogy on p.276 involving Boston Cream Pie

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

Ch. 7-8 Textbook Assignment due

5

Work period

6

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

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

7

Work period

Ch. 9-10 Textbook Assignment due

8

Test day

Statistics Test (Chapters 2 – 12)

9 – 17

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

Work period

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)

Work period

22

Interim  Report Cards

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

25

Work period

26

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

Ch. 14-15 Assignment due

27

OSSLT

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

28

Parents Night

Work period

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

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

April 1

Work period

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

Ch. 14—17 Quiz

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

Work period

8

Constructing Simulations using Excel and Fathom

9

Work period

10

FGH

*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

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

11

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

12

*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

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

1 absent

15

Work period

7 absent (CCC)

16

*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

**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

17

Work period

1 absent (band)

18

Work period

19

Good Friday

22

Easter Monday

23

*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

**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

Quiz: Ch. 18-22

1 absent (GSuite cert)

24

Work period

25 Full Disclosure

*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

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

2 absent (DECA)

26 Holy Friday

Work period

2 absent (DECA)

29

*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.

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

2 absent (DECA)

30

Work period

2 absent (DECA)

May 1

*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

2 absent (DECA)

2

Prom; CEMC marking

Work period

3 absent (DECA; mt biking)

3

CEMC marking

PA Day

6

7

5 absent (AP Physics)

8

Review for test

9

Review for AP Exam (Multiple Choice)

5 absent (AP Chem, Psych)

10

Test 2:  Statistical Inference (chapters 18 – 25)

13

Review  (Full response – short answer)

4 absent (AP Bio, Physics C)

14

2 absent (AP Calc)

15

Review (Full response –big answer) Day 2

3 absent (AP Eng; mt biking)

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

4 absent (AP CS, Econ)

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

1 absent (mt biking)

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

1 absent (personal)

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

Chapters 6.1 – 6.5

1 absent (personal)

4

Choose & arrange type questions

Work period

Handout, Review Probability

1 absent (mt biking)

5

Eid-ul-Fitr

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”.

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

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

6

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

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

Work period

·         Gambling Case Study

·         Poker

·         Blackjack

·         Roulette

Lotteries

11

Test 3 – Combinatorics & Probability

12

Dice Assignment II due

13

14

Review for Exam

Final exam review

Read the sample Final Exam cover page.

1 absent (Carnival?)

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

PA Day

28

PA Day

Mon July 1st