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IHS AP Statistics Chapter1 Exploring Data MP1

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Ch1 Exploring Data

Class Introduction Getting to Know Your Textbook Stat Survey Ch1 Introduction: Data Analysis: Making Sense of Data HW Vocab Notes Ch1 Intro and 1.1 HW #1.0: page 6 (1, 3, 5, 7, 8)

1.1 Analyzing Categorical Data HW #1.1A: page 21 (11, 17, 18) HW #1.1B: page 22 (20, 22, 23, 25, 27–34)

1.2 Displaying Quantitative Data with Graphs HW #1.2A: page 41 (37, 39, 43, 45, 47) HW #1.2B: page 43 (51, 53, 55, 59–62)

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Ch1 Exploring Data

1.2 Displaying Quant. Data with Graphs HW #1.2A: page 41 (37, 39, 43, 45, 47) HW #1.2B: page 43 (51, 53, 55, 59–62)

1.3 Describing Quantitative Data with Numbers HW #1.3A: page 47 (69–74), page 69 (79, 81, 83, 85, 86, 88, 89, 91, 93, 94a) HW #1.3B: page 71 (97, 99, 101–105, 107–110)

Ch.1 Review HW: Chapter Review Exercises (p76)

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Ch2 Modeling Distributions of Data

Labor Day

FRAPPY! Practice HW: Ch1 AP Statistics Practice Test (p78)

Chapter 1 Test

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Ch2 Modeling Distributions of Data

2.1 Describing Location in a Distribution HW #2.1A: page 99 (1, 5, 9, 11, 13, 15) HW #2.1B page 101 (17–23 odd, 32)

2.2 Density Curves and Normal Dists – Day1 HW #2.2A: page 102 (25–30), page 128 (33-45 odd) HW #2.2B: page 129 (47–57 odd)

2.2 Density Curves and Normal Distributions – Day2 HW #2.2C page 130 (54–60 even, 68–73)

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Ch2 Modeling Distributions of Data

2.2 Density Curves and Normal Distributions – Day2 HW #2.2C page 130 (54–60 even, 68–73)

Ch.2 Review HW: Chapter Review Exercises (p136) HW: Ch2 AP Statistics Practice Test (p137)

Chapter 2 Test

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Ch3 Describing Relationships

3.1 Scatterplots and Correlation

3.2 Scatterplots and Correlation - Day1

3.2 Scatterplots and Correlation – Day2

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Ch1 Intro: Data Analysis: Making Sense of Data

Sec 1.1 Analyzing Categorical Data

Vocabulary frequency table relative frequency

table pie chart bar graph two way table

marginal

distribution conditional

distribution segmented bar

graph association

Learning Objectives DISPLAY categorical data with a bar graph. Decide if it would be

appropriate to make a pie chart. IDENTIFY what makes some graphs of categorical data deceptive. CALCULATE and DISPLAY the marginal distribution of a

categorical variable from a two-way table. CALCULATE and DISPLAY the conditional distribution of a

categorical variable for a particular value of the other categorical variable in a two-way table.

DESCRIBE the association between two categorical variables by comparing appropriate conditional distributions.

Sec 1.2 Displaying Quantitative Data with Graphs

Vocabulary dotplot skewed right skewed left symmetric bimodal

unimodal stemplots back to back

stemplot histogram

Learning Objectives MAKE and INTERPRET dotplots and stemplots of quantitative data. DESCRIBE the overall pattern (shape, center, and spread) of a

distribution and IDENTIFY any major departures from the pattern (outliers).

IDENTIFY the shape of a distribution from a graph as roughly symmetric or skewed.

MAKE and INTERPRET histograms of quantitative data. COMPARE distributions of quantitative data using dotplots, stemplots or

histograms.

Sec 1.3 Describing Quantitative Data with Numbers

Vocabulary mean median first quartile third quartile interquartile

range outliers

formula for finding

outliers five number summary boxplot standard deviation variance resistant

Learning Objectives CALCULATE measures of center (mean, median). CALCULATE and INTERPRET measures of spread (range, IQR,

standard deviation). CHOOSE the most appropriate measure of center and spread in a

given setting. IDENTIFY outliers using the 1.5 × IQR rule. MAKE and INTERPRET boxplots of quantitative data. USE appropriate graphs and numerical summaries to compare

distributions of quantitative variables.

Vocabulary individuals variable categorical variable quantitative variable distribution

Learning Objectives IDENTIFY the individuals and variables in a set of data. CLASSIFY variables as categorical or quantitative.

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IHS AP Statistics Name: _____________________________ Per: ______ Ch1 Intro: Data Analysis: Making Sense of Data Discuss and write below ideas on how you might use this data to answer the question “Does the presence of a pet of friend reduce heart rate during a stressful task”? Think about how you would summarize the data (will you use tables, graphs, and if so what will they look like) and what your conclusion will be (how will you justify your answer).

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p2–4 What’s the difference between categorical and quantitative variables? Do we ever use numbers to describe the values of a categorical variable? Do we ever divide the distribution of a quantitative variable into categories? What is a distribution? Example: US Census Data Here is information about 10 randomly selected US residents from the 2000 census.

State Number of Family

Members Age Gender

Marital Status

Total Income

Travel time to work

Kentucky 2 61 Female Married 21000 20

Florida 6 27 Female Married 21300 20

Wisconsin 2 27 Male Married 30000 5

California 4 33 Female Married 26000 10

Michigan 3 49 Female Married 15100 25

Virginia 3 26 Female Married 25000 15

Pennsylvania 4 44 Male Married 43000 10

Virginia 4 22 Male Never married/ single 3000 0

California 1 30 Male Never married/ single 40000 15

New York 4 34 Female Separated 30000 40

Problem: (a) Who are the individuals in this data set? (b) What variables are measured? Identify each as categorical or quantitative. (c) Describe the individual in the first row. Solution:

HW #1.0: page 6 (1, 3, 5, 7, 8)

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Sec 1.1 Analyzing Categorical Data p7–11 What is the difference between a data table, a frequency table, and a relative frequency table? When is it better to use

relative frequency? Example: College Majors Here is the distribution of bachelor’s degrees awarded in 2010, according to http://nces.ed.gov/programs/digest/d11/tables/dt11_286.asp:

Major Number

of degrees

Percent of

degrees

Business 358,293 21.7

Social sciences/history 172,780 10.5

Health professions 129,634 7.9

Education 101,265 6.1

Psychology 97,216 5.9

Visual and performing arts 91,802 5.6

Biological and biomedical sciences 86,400 5.2

Communication and related programs 81,266 4.9

Engineering 72,654 4.4

English language and literature 53,231 3.2

Other 405,473 24.6

Total 1,650,014 100.0

Problem: Find the individuals, variable, frequencies, and relative frequencies. Solution: What is the most important thing to remember when making pie charts and bar graphs? Why do statisticians prefer

bar graphs? When is it inappropriate to use a pie chart?

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Example: What Do Teens Post? Here are the percentages of 12- to 17-year-olds who post various types of personal information on their social media profiles, according to the Pew Internet Parent/Teen Privacy Survey in 2012.

Type of personal information Percent who post

Photo of themselves 91

School name 71

City or town where they live 71

Email address 53

Cell phone number 20

Problem: (a) Make a well-labeled bar graph to display the data. Describe what you see. (b) Would it be appropriate to make a pie chart for these data? Explain. Solution: What are some common ways to make a misleading graph? Example: A misleading graph? Problem1: In the 2008–2009 regular season, basketball player Dwayne Wade averaged 7.5 assists per game and 2.2 steals per game. Explain what is wrong with the following graph and how to make it better.

Problem2: What is wrong with the following graph?

HW #1.1A: page 21 (11, 17, 18)

Solution:

Solution:

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p12–18 What is a two-way table? What is a marginal distribution? Example: Cell phones The Pew Research Center asked a random sample of 2024 adult cell phone owners from the United States which type of cell phone they own: iPhone, Android, or other (including non-smart phones). Here are the results, broken down by age category. http://pewinternet.org/Reports/2013/Smartphone-Ownership-2013.aspx

18-34 35-54 55+ Total

iPhone 169 171 127 467

Android 214 189 100 503

Other 134 277 643 1054

Total 517 637 870 2024

Problem: (a) Use the cell phone data to calculate the marginal distribution (in percents) of type of cell phone. (b) Make a graph to display the marginal distribution. Describe what you see. Solution: What is a conditional distribution? How do we know which variable to condition on? Example: Cell phones Problem: Use the cell phone data to calculate the conditional distribution of cell phone type for the 18- to 34-year-olds. Solution:

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What is a segmented bar graph? Why are they good to use? What does it mean for two variables to have an association? How can you tell by looking at a graph? Example: Cell phones Problem: (a) Explain what it would mean if there was no association between age and cell phone type. (b) Based on the cell phone data, is there evidence of a difference in the distribution of cell phone ownership for the three age groups? Justify your answer. (c) Based on this data, can we conclude there is an association between age and cell phone type? Justify your answer. Solution: HW #1.1B: page 22 (20, 22, 23, 25, 27–34)

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Sec 1.2 Displaying Quantitative Data with Graphs Brian and Jessica have decided to move and are considering seven different cities. The dotplots below show the daily high temperatures in June, July, and August for each of these cities. Help them pick a city by answering the questions below.

1. What is the most important difference between cities A, B, and C?

2. What is the most important difference between cities C and D?

3. What are two important differences between cities D and E?

4. What is the most important difference between cities C, F, and G?

AB

CD

EF

G

50 60 70 80 90 100 110

Collection 1 Dot Plot

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p25–27 Example: Frozen Pizza Consumer Reports magazine rated frozen pizza in their January 2011 issue. Here are the amounts of sodium (in mg) in a single serving of 16 different brands of cheese pizza. 580 740 850 850 870 850 670 670 630 690 780 610 790 570 700 640 Problem: Make a dotplot describing this data. Solution: When describing the distribution of a quantitative variable, what characteristics should be addressed? Example: Frozen Pizza Here are the number of calories per serving for 16 brands of frozen cheese pizza, along with a dotplot of the data. 340 340 310 320 310 360 350 330 260 380 340 320 360 290 320 330 Problem: Describe the shape, center, and spread of the distribution. Are there any outliers? Solution:

Calories

260 280 300 320 340 360 380 400

Frozen Pizza Dot Plot

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p27–29 Briefly illustrate the following distribution shapes:

Symmetric Skewed right Skewed left

Unimodal Bimodal Uniform Example: Die rolls and frozen pizza Here are dotplots for two different sets of quantitative data. Problem: Describe the distribution for each dataset. Solution: p29–30 What is the most important thing to remember when you are asked to compare two distributions? Example: Energy Cost: Top vs. Bottom Freezers How do the annual energy costs (in dollars) compare for refrigerators with top freezers and refrigerators with bottom freezers? The data below are from the May 2010 issue of Consumer Reports. Problem: Compare the distributions of energy cost for these two types of refrigerators. Solution:

DieRoll

0 2 4 6 8 10

Collection 2 Dot Plot

Fiber

1 2 3 4 5

Frozen Pizza Dot Plot

EnergyCost

Ty

pe

14012611298847056

bottom

top

Dotplot of EnergyCost vs Type

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p31–32 What is the most important thing to remember when making a stemplot? Example: Who’s Taller? Which gender is taller, males or females? A sample of 14-year-olds from the United Kingdom was randomly selected using the CensusAtSchool website. Here are the heights of the students (in cm). Male: 154, 157, 187, 163, 167, 159, 169, 162, 176, 177, 151, 175, 174, 165, 165, 183, 180 Female: 160, 169, 152, 167, 164, 163, 160, 163, 169, 157, 158, 153, 161, 165, 165, 159, 168, 153, 166, 158, 158, 166 Problem: Make a back-to-back stemplot and compare the distributions. Solution: HW #1.2A: page 41 (37, 39, 43, 45, 47)

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1.2 Histograms p33–36 How do you make a histogram? Example: NBA Scoring Averages The following table presents the average points scored per game (PPG) for the 30 NBA teams in the 2012–2013 regular season.

Team PPG Team PPG Team PPG

Atlanta Hawks 98.0 Houston Rockets 106.0 Oklahoma City Thunder 105.7

Boston Celtics 96.5 Indiana Pacers 94.7 Orlando Magic 94.1

Brooklyn Nets 96.9 Los Angeles Clippers 101.1 Philadelphia 76ers 93.2

Charlotte Bobcats 93.4 Los Angeles Lakers 102.2 Phoenix Suns 95.2

Chicago Bulls 93.2 Memphis Grizzlies 93.4 Portland Trail Blazers 97.5

Cleveland Cavaliers 96.5 Miami Heat 102.9 Sacramento Kings 100.2

Dallas Mavericks 101.1 Milwaukee Bucks 98.9 San Antonio Spurs 103.0

Denver Nuggets 106.1 Minnesota Timberwolves 95.7 Toronto Raptors 97.2

Detroit Pistons 94.9 New Orleans Hornets 94.1 Utah Jazz 98.0

Golden State Warriors 101.2 New York Knicks 100.0 Washington Wizards 93.2

Problem: Make a dotplot to display the distribution of points per game. Then, use your dotplot to make a histogram of the distribution. Solution: p38–41 Why would we prefer a relative frequency histogram to a frequency histogram? HW #1.2B: page 43 (51, 53, 55, 59–62)

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Sec 1.3 Describing Quantitative Data with Numbers p48–50

What is the difference between x and ?

Example: McDonald’s Fish and Chicken Sandwiches Here are data on the amount of fat (in grams) in 9 different McDonald’s fish and chicken sandwiches, along with a stemplot:

Sandwich Fat (g)

Filet-O-Fish® 19

McChicken® 16

Premium Crispy Chicken Classic Sandwich 22

Premium Crispy Chicken Club Sandwich 33

Premium Crispy Chicken Ranch Sandwich 27

Premium Grilled Chicken Classic Sandwich 9

Premium Grilled Chicken Club Sandwich 20

Premium Grilled Chicken Ranch Sandwich 14

Southern Style Crispy Chicken Sandwich 19

0 9

1 4

1 699

2 02

2 7

3 3

Problem: (a) Find the mean amount of fat for fish and chicken sandwiches. (b) The Premium Crispy Chicken Club Sandwich is a potential outlier. How much does this one sandwich increase the mean? Solution: What is a resistant measure? Is the mean a resistant measure of center? How can you estimate the mean of a histogram or dotplot?

Key: 3|3 represents

33 grams of fat in a

McDonald’s fish or

chicken sandwich.

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p51–53 Example: McDonald’s Fish and Chicken Sandwiches Problem: (a) Find the median amount of fat for fish and chicken sandwiches. Example: McDonald’s Beef Sandwiches Here are data for the amount of fat (in grams) for McDonald’s beef sandwiches.

Sandwich Fat

Big Mac® 29

Cheeseburger 12

Daily Double 24

Double Cheeseburger 23

Double Quarter Pounder® with cheese 43

Hamburger 9

McDouble 19

McRib® 26

Quarter Pounder® Bacon and Cheese 29

Quarter Pounder® Bacon Habanero Ranch 31

Quarter Pounder® Deluxe 27

Quarter Pounder® with Cheese 26

Problem: (a) Make a stemplot of the data. Be sure to include a key. (b) Find the median by hand. Show your work. Solution:

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Is the median a resistant measure of center? Explain. How does the shape of a distribution affect the relationship between the mean and the median? p53–55

What is the range? Is it a resistant measure of spread? Explain. What are quartiles? How do you find them? What is the interquartile range (IQR)? Is the IQR a resistant measure of spread? Example: McDonald’s Fish and Chicken Sandwiches Problem: Calculate the median and the IQR. Solution: Example: McDonald’s Beef Sandwiches Problem: Find and interpret the IQR for the distribution of fat in McDonald’s beef sandwiches. Solution:

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p56–57 What is an outlier? How do you identify them? Example: McDonald’s Beef Sandwiches Problem: Determine whether there are any outliers in the distribution of fat for McDonald’s beef sandwiches. Solution: p57–59 What is the five-number summary? How is it displayed? Example: The Previous Home Run King Here are the number of home runs that Hank Aaron hit in each of his 23 seasons:

13 27 26 44 30 39 40 34 45 44 24 32 44 39 29 44 38 47 34 40 20 12 10

Problem: Make a boxplot for these data. Solution: Example: McDonald’s Fish/Chicken and Beef Sandwiches Problem: Draw parallel boxplots for the beef and chicken/fish sandwich data. Compare these distributions. Solution: HW #1.3A: page 47 (69–74), page 69 (79, 81, 83, 85, 86, 88, 89, 91, 93, 94a)

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1.3 Standard Deviation In the distribution below, how far are the values from the mean, on average?

What does the standard deviation measure? What are some similarities and differences between the range, IQR, and standard deviation? p60–62 Example: Foot Lengths Here are the foot lengths (in centimeters) for a random sample of seven 14-year-olds from the United Kingdom:

25, 22, 20, 25, 24, 24, 28 Problem:

(a) Find the mean x , deviations from the mean (xi – x ) and the squared deviations from the mean (xi – x )2:

(b) Find the “average” squared deviation and the standard deviation. Interpret the standard deviation. Solution: How is the standard deviation calculated? What is the variance? What are some properties of the standard deviation?

Data

0 1 2 3 4 5 6 7 8

Collection 1 Dot Plot

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Example: How long do you spend doing HW? A random sample of 5 students was asked how many minutes they spent doing HW the previous night. Here are their responses (in minutes): 0, 25, 30, 60, 90. Problem: Calculate and interpret the standard deviation. Solution: p63–66 What factors should you consider when choosing summary statistics? Example: Who Has More Contacts—Males or Females? The following data show the number of contacts that a sample of high school students had in their cell phones. What conclusion can we draw? Give appropriate evidence to support your answer.

Male: 124 41 29 27 44 87 85 260 290 31 168 169 167 214 135 114 105 103 96 144 Female: 30 83 116 22 173 155 134 180 124 33 213 218 183 110

Problem: What conclusion can we draw? Give appropriate evidence to support your answer. Solution: HW #1.3B: page 71 (97, 99, 101–105, 107–110)